Based on the standard seven-step problem-solving strategy, identify the specific name of the step the HR director is currently performing.

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A systematic, seven-step strategy helps in solving algebraic word problems effectively:

1. **Read** the problem carefully to ensure all words and ideas are understood.
2. **Identify** exactly what you are looking for.
3. **Name** what you are looking for by choosing a variable to represent that quantity.
4. **Translate** the situation into an equation. It can be helpful to first restate the problem in a single sentence containing the important information.
5. **Solve** the equation using appropriate algebraic techniques.
6. **Check** the calculated answer against the original problem to make sure it makes logical sense.
7. **Answer** the original question with a complete, clearly written sentence.

Problem-Solving Strategy for Word Problems

To see the seven-step problem-solving strategy in action, consider the following word problem: *Randell paid \$28,675 for his new car. This was \$875 less than the sticker price. What was the sticker price of the car?*

1. **Read**: Understand that the problem asks for the original sticker price based on the price paid and the discount amount.
2. **Identify**: We are looking for the sticker price of the car.
3. **Name**: Let $s$ represent the sticker price of the car.
4. **Translate**: Restate the problem: \$28,675 is \$875 less than the sticker price. As an equation: $}28,675 = s - 875${.
5. **Solve**: Add 875 to both sides to isolate the variable $s$:
${}28,675 + 875 = s - 875 + 875$
${}29,550 = s$
6. **Check**: Is \$875 less than \$29,550 equal to \$28,675? Yes ($}29,550 - 875 = 28,675${).
7. **Answer**: The sticker price of the car was \$29,550.

Example: Solving a Word Problem for a Car's Sticker Price

Apply the problem-solving strategy to find a unit cost using the Division Property of Equality.

**Problem:** Denae bought $$6$$ pounds of grapes for \$10.74. What was the cost of one pound of grapes?

1. **Identify** what to find: the cost of $$1$$ pound of grapes.
2. **Name** the unknown: Let $$c$$ = the cost of one pound.
3. **Translate** into a single sentence: "The cost of $$6$$ pounds is \$10.74." This becomes the equation $$6c = 10.74$$.
4. **Solve** by dividing both sides by $$6$$ (Division Property of Equality):

$$\frac{6c}{6} = \frac{10.74}{6}$$

$$c = 1.79$$

5. **Answer**: The grapes cost \$1.79 per pound.
6. **Check** by substituting back: Does $$6(1.79) = 10.74$$?

$$6(1.79) \stackrel{?}{=} 10.74$$

$$10.74 = 10.74 \checkmark$$

The answer is confirmed. This example illustrates how a real-world multiplication relationship — total cost equals the number of units times the cost per unit — translates into an equation of the form $$nc = T$$, which is solved by dividing both sides by the number of units.

Solving a Word Problem for the Cost Per Pound of Grapes

Apply the problem-solving strategy to find an original price when only a fractional portion of it is known, using the Multiplication Property of Equality.

**Problem:** Andreas purchased a used car for \$12,000. Since the car was $$4$$ years old, this price was $$\frac{3}{4}$$ of the original price when it was new. What was the original price of the car?

1. **Identify** what to find: the original price of the car when it was new.
2. **Name** the unknown: Let $$p$$ = the original price.
3. **Translate** into a sentence and equation: "\$12,000 is $$\frac{3}{4}$$ of the original price." This becomes the equation $$12{,}000 = \frac{3}{4}p$$.
4. **Solve** by multiplying both sides by $$\frac{4}{3}$$, the reciprocal of the fractional coefficient $$\frac{3}{4}$$:

$$\frac{4}{3}(12{,}000) = \frac{4}{3} \cdot \frac{3}{4}p$$

On the right side, $$\frac{4}{3} \cdot \frac{3}{4} = 1$$ by the inverse property of multiplication, leaving just $$p$$. On the left side, $$\frac{4}{3} \cdot 12{,}000 = 16{,}000$$:

$$16{,}000 = p$$

5. **Check** by substituting back: Is $$\frac{3}{4}$$ of \$16,000 equal to \$12,000?

$$\frac{3}{4} \cdot 16{,}000 \stackrel{?}{=} 12{,}000$$

$$12{,}000 = 12{,}000 \checkmark$$

6. **Answer**: The original price of the car was \$16,000.

This example illustrates how the phrase "fraction *of* a quantity" translates into multiplication by that fraction. When the known value equals a fraction times the unknown, the equation takes the form $$\text{known} = \frac{a}{b} \cdot p$$, and the unknown is isolated by multiplying both sides by the reciprocal $$\frac{b}{a}$$. This pattern arises frequently in real-world problems involving discounts, depreciation, or partial quantities.

Solving a Word Problem for a Car's Original Price

When a word problem involves a known formula, the general seven-step problem-solving strategy is adapted so that the **Translate** step uses the formula directly rather than constructing an equation from scratch. The revised steps are:

1. **Read** the problem and make sure all the words and ideas are understood.
2. **Identify** what you are looking for.
3. **Name** the unknown by choosing a variable to represent it.
4. **Translate** by writing the appropriate formula for the situation and substituting in the given information.
5. **Solve** the resulting equation using standard algebra techniques.
6. **Check** the answer in the original problem to make sure it is reasonable.
7. **Answer** the question with a complete sentence.

Organizing the known and unknown quantities into a small chart before substituting can help keep the information clear. For instance, when working with $$d = rt$$, listing which of $$d$$, $$r$$, and $$t$$ are given and which is unknown makes it straightforward to substitute and solve.

Strategy for Solving Formula-Based Applications

Apply the seven-step problem-solving strategy to a word problem in which one quantity is described using two combined operations — multiplication and addition — applied to the unknown.

**Problem:** In a study group, the number of girls was three more than twice the number of boys. There were $$11$$ girls. How many boys were in the study group?

1. **Read** the problem carefully and confirm that every word is understood.
2. **Identify** what to find: the number of boys in the study group.
3. **Name** the unknown: Let $$n$$ = the number of boys.
4. **Translate** into an equation: The phrase "three more than twice the number of boys" combines two operations — "twice" signals multiplication by $$2$$, and "three more than" signals adding $$3$$ to that product. So the number of girls equals $$2n + 3$$. Since there are $$11$$ girls:

$$11 = 2n + 3$$

5. **Solve** using a two-step process. First, subtract $$3$$ from both sides to undo the addition:

$$11 - 3 = 2n + 3 - 3$$

$$8 = 2n$$

Then divide both sides by $$2$$ to isolate $$n$$:

$$\frac{8}{2} = \frac{2n}{2}$$

$$4 = n$$

6. **Check**: Is $$4$$ boys reasonable for a study group? Yes. Does "three more than twice $$4$$" equal $$11$$? Twice $$4$$ is $$8$$; three more than $$8$$ is $$11$$. $$\checkmark$$
7. **Answer**: There were $$4$$ boys in the study group.

This example shows how the phrase "more than twice" combines multiplication and addition into a single algebraic expression, producing a two-step equation that requires both subtraction and division to solve. Unlike problems where the translation involves only one operation, multi-operation phrases demand careful attention to the order in which the operations are applied to the unknown.

Solving a Word Problem for the Number of Boys in a Study Group

**Number problems** are a category of word problems that provide verbal clues about one or more unknown numbers, and the goal is to use those clues to set up and solve an algebraic equation. Unlike most real-world word problems — which involve contexts such as prices, distances, or quantities of physical objects — number problems are abstract: they deal with numbers themselves rather than with a practical scenario. Because of this simplicity, number problems serve as an excellent first application of the seven-step problem-solving strategy. They allow students to focus on the core skills of identifying operation keywords (such as "difference," "sum," and "twice"), translating verbal clues into an equation, solving the equation, and verifying the result — all without the added complexity of interpreting a real-world context.

Number Problems

When a word problem asks for two or more unknown numbers, it may seem natural to assign each unknown its own separate variable. However, at the introductory algebra level, equations are solved for a single variable only. The strategy for handling multiple unknowns is to **express every unknown quantity in terms of one chosen variable** by using the relationships stated in the problem. This requires careful reading to identify how the numbers relate to one another. For example, if one number is described as "five more than" another, the first number can be represented as $$n$$ and the second as $$n + 5$$. By writing all quantities through a single variable, the resulting equation contains only one unknown and can be solved with standard algebraic techniques.

Expressing Multiple Unknowns in Terms of a Single Variable

Apply the seven-step problem-solving strategy to a real-world word problem in which two people's earnings add up to a known total, and one earning is described using the phrase "less than twice" the other — combining multiplication and subtraction into a single expression.

**Problem:** A married couple together earns $$\$110{,}000$$ a year. The wife earns $$\$16{,}000$$ less than twice what her husband earns. What does the husband earn?

1. **Read** the problem carefully.
2. **Identify** what to find: the husband's annual earnings.
3. **Name** the unknown: Let $$h$$ = the amount the husband earns. The phrase "$$\$16{,}000$$ less than twice what her husband earns" combines two operations: *twice* signals multiplication by $$2$$, and *$$\$16{,}000$$ less than* signals subtraction. The wife's earnings are therefore $$2h - 16{,}000$$.
4. **Translate** into an equation: Together the husband and wife earn $$\$110{,}000$$, so:
$$h + (2h - 16{,}000) = 110{,}000$$

5. **Solve** the equation. Combine the like terms $$h + 2h = 3h$$:
$$3h - 16{,}000 = 110{,}000$$
Add $$16{,}000$$ to both sides:
$$3h = 126{,}000$$
Divide both sides by $$3$$:
$$h = 42{,}000$$
Find the wife's earnings: $$2(42{,}000) - 16{,}000 = 84{,}000 - 16{,}000 = 68{,}000$$.

6. **Check**: Does $$\$42{,}000 + \$68{,}000 = \$110{,}000$$? $$110{,}000 = 110{,}000$$ $$\checkmark$$

7. **Answer**: The husband earns $$\$42{,}000$$ a year.

This example transitions from abstract number problems to a practical financial scenario while using the same algebraic techniques. The phrase "less than twice" produces a subtraction-from-a-multiple expression ($$2h - 16{,}000$$), and the equation $$h + (2h - 16{,}000) = 110{,}000$$ requires combining like terms, adding a constant to both sides, and dividing — three steps that mirror the structure seen in earlier number problems. Both unknowns are expressed through a single variable by using the stated relationship between the couple's earnings.

Solving a Combined-Earnings Word Problem Using 'Less Than Twice'

Apply the seven-step problem-solving strategy to a percent application in which the **amount** (the tip) is the unknown.

**Problem:** Dezohn's restaurant bill was \$68.50, and he wants to leave an $$18\%$$ tip. How much should the tip be?

1. **Identify** what to find: the dollar amount of the tip.
2. **Name** the unknown: Let $$t$$ = the tip amount.
3. **Translate** into a percent sentence and equation: "The tip is $$18\%$$ of the total bill" becomes

$$t = 0.18 \times 68.50$$

4. **Solve** by multiplying:

$$t = 12.33$$

5. **Check** — a quick reasonableness test: $$20\%$$ of \$70 would be \$14, so \$12.33 for $$18\%$$ of \$68.50 is sensible.
6. **Answer:** Dezohn should leave a tip of \$12.33.

This problem is a "find the amount" percent equation — the percent and the base are both known, so the variable is already isolated after translation and only a single multiplication step is needed. Choosing the letter $$t$$ (for "tip") makes the equation easier to read and interpret in context.

Solving a Tip Calculation Using a Percent Equation

Apply the seven-step problem-solving strategy to a percent application in which the **base** (the whole) is the unknown.

**Problem:** One serving of breakfast cereal provides $$85$$ mg of potassium, which is $$2\%$$ of the recommended daily amount. What is the total recommended daily amount of potassium?

1. **Identify** what to find: the total recommended daily amount of potassium.
2. **Name** the unknown: Let $$a$$ = the total amount of potassium recommended daily.
3. **Translate** into a percent sentence and equation: "$$85$$ mg is $$2\%$$ of the total amount" becomes

$$85 = 0.02 \times a$$

4. **Solve** by dividing both sides by $$0.02$$:

$$\frac{85}{0.02} = a$$

$$a = 4{,}250$$

5. **Check** — $$2\%$$ is a small percent, and $$85$$ is indeed a small portion of $$4{,}250$$, so the answer is reasonable.
6. **Answer:** The total recommended daily amount of potassium is $$4{,}250$$ mg.

This problem is a "find the base" percent equation. After translation the variable $$a$$ is multiplied by the decimal coefficient $$0.02$$, so dividing both sides by that coefficient — using the Division Property of Equality — isolates the unknown and reveals the whole amount.

Finding the Total Recommended Daily Amount of Potassium

Apply the seven-step problem-solving strategy to a percent application in which the **percent** is the unknown.

**Problem:** Each gourmet brownie contains $$480$$ total calories, of which $$240$$ calories come from fat. What percent of the total calories is from fat?

1. **Identify** what to find: the percent of total calories that come from fat.
2. **Name** the unknown: Let $$p$$ = the percent (to be found first in decimal form).
3. **Translate** into a percent sentence and equation: "What percent of $$480$$ is $$240$$?" becomes

$$p \times 480 = 240$$

4. **Solve** by dividing both sides by $$480$$:

$$\frac{480p}{480} = \frac{240}{480}$$

$$p = 0.5$$

5. **Convert to percent form:** $$p = 50\%$$
6. **Check** — $$240$$ is exactly half of $$480$$, so $$50\%$$ is clearly correct.
7. **Answer:** Of the total calories in each brownie, $$50\%$$ come from fat.

This is a "find the percent" equation. The variable $$p$$ represents the unknown percent, which appears as a decimal coefficient multiplying the base. After dividing both sides by the base, the resulting decimal must be converted to percent form (move the decimal point two places to the right and attach $$\%$$) to answer the original question.

Finding the Percent of Calories from Fat

**Mixture problems** are a category of word problems in which two or more items, each having a different value, are combined. The objective is to determine some unknown quantity — such as the number of items, their individual values, or the combined total value — by setting up and solving an algebraic equation. The underlying model is widely used in everyday life and across professions: grocers and bartenders use it to set fair prices on blended products, while chemists, investment bankers, and landscapers apply the same principle whenever different-valued components must be mixed. Because mixture problems deal with concrete, real-world items (coins, foods, solutions, investments), they build on the abstract skills developed in number problems by adding the challenge of tracking both quantities and per-unit values simultaneously.

Mixture Problems

When solving real-world word problems that involve systems of linear equations, the general seven-step problem-solving strategy used for single-equation word problems is adapted so that the **Translate** step produces a **system of equations** rather than a single equation, and the **Solve** step uses a system-solving technique (such as graphing, substitution, or elimination) rather than standard one-variable algebra. The steps are:

1. **Read** the problem. Make sure all the words and ideas are understood.
2. **Identify** what you are looking for.
3. **Name** what you are looking for. Choose variables to represent those quantities.
4. **Translate** the problem into a **system of equations**.
5. **Solve** the system of equations using good algebra techniques.
6. **Check** the answer in the problem and make sure it makes sense.
7. **Answer** the question with a complete sentence.

The key adaptation is in Steps 3, 4, and 5. Because systems problems typically involve **two** unknown quantities, Step 3 assigns a separate variable to each unknown. Step 4 then produces two equations — one for each relationship described in the problem — forming a system. Step 5 solves this system using whichever technique is appropriate, such as graphing, substitution, or elimination. Some application problems translate directly into equations in standard form, making the elimination method especially convenient for those cases.

An additional benefit of the systems approach is that some people find setting up word problems with two variables easier than with just one variable — choosing variable names is simpler when each unknown gets its own letter, rather than having to express all quantities through a single variable.

Problem-Solving Strategy for Systems of Linear Equations

When a word problem that translates into a quadratic equation is solved algebraically, the factoring process may produce two solutions — including a negative value. In some real-world contexts, a negative answer does not make sense (for example, a length, a count of objects, or an elapsed time cannot be negative). When this happens, the negative solution is a valid algebraic answer to the equation but must be **discarded** because it does not fit the situation described in the problem. This is why the **Check** step in the problem-solving strategy requires more than verifying the algebra: the solver must also confirm that each answer is reasonable within the original real-world context. Not every quadratic application produces unrealistic negatives — for instance, a problem about the product of two consecutive integers may yield both a positive and a negative pair that are both meaningful.

Discarding Unrealistic Negative Solutions in Applications

A retail manager is calculating the necessary markup for a new product line to meet a specific profit goal. To solve this word problem using the standard seven-step algebraic strategy, arrange the first four steps in the correct chronological order.

A project manager is training a new hire on the company's standard seven-step algebraic strategy for solving budget-related word problems. Match each step of the strategy with its correct description to ensure the team follows a consistent process.

A payroll specialist is using the standard seven-step problem-solving strategy to determine a staff member's total overtime compensation. After solving the algebraic equation, the specialist must perform the 'Check' step. What is the primary objective of this step?

A project coordinator has successfully solved an algebraic equation to determine a department's budget allocation and has verified that the result is logically sound. According to the seven-step problem-solving strategy, what specific final action must the coordinator take to conclude the process?

Finalizing the Algebraic Problem-Solving Process

A project manager is using the standard seven-step problem-solving strategy to calculate the total budget for a new initiative. True or False: The 'Identify' step of this strategy involves choosing a specific variable, such as 'x', to represent the unknown budget amount.

Recruitment Budget Analysis

A logistics coordinator is following a seven-step strategy to calculate the total number of shipping containers needed for a large export order. After choosing a variable to represent the unknown quantity, the coordinator converts the written requirements of the problem into a mathematical equation. This fourth step in the problem-solving strategy is the ____ step.

Your department is implementing a 'Standard Operating Procedure' for all data analysts to ensure that algebraic word problems regarding project budgets are solved consistently and accurately. To assist with the transition, you have been asked to document the company's approved seven-step problem-solving strategy. List all seven steps of the strategy in their correct order and provide a brief description of the specific action required in each step.

Standardizing the Problem-Solving Workflow

A procurement officer is using the standard seven-step algebraic strategy to determine the unit cost of a large supply order. In the third step of this process, known as 'Name', what specific action is required?

A training coordinator is using a standard seven-step strategy to calculate the number of workshops needed for a department expansion. After successfully translating the word problem into a mathematical equation, what is the next step the coordinator must perform according to this strategy?

Apply the problem-solving strategy to find two consecutive odd integers whose product is $$323$$.

1. **Identify and Name**: Let $$n$$ represent the first odd integer. The next consecutive odd integer is $$n + 2$$.
2. **Translate**: The product of the two consecutive odd integers is $$323$$, which translates to the equation $$n(n + 2) = 323$$.
3. **Solve**: Distribute $$n$$ to get $$n^2 + 2n = 323$$. Bring all terms to one side to write the quadratic equation in standard form: $$n^2 + 2n - 323 = 0$$. Factor the trinomial to obtain $$(n - 17)(n + 19) = 0$$. Using the Zero Product Property, solve to find $$n = 17$$ or $$n = -19$$.

There are two sets of solutions:
- If the first integer is $$17$$, the next consecutive odd integer is $$17 + 2 = 19$$.
- If the first integer is $$-19$$, the next consecutive odd integer is $$-19 + 2 = -17$$.

4. **Check**: $$17 \cdot 19 = 323$$ and $$-19(-17) = 323$$. Both pairs are valid solutions.
5. **Answer**: The consecutive odd integers are $$17$$ and $$19$$, and $$-19$$ and $$-17$$.

Solving for Two Consecutive Odd Integers Whose Product is $$323$$

Apply the problem-solving strategy to find two consecutive odd integers whose product is $$255$$.

Let $$n$$ be the first odd integer, making the next consecutive odd integer $$n + 2$$.
The product of the two integers is $$255$$, leading to the algebraic equation: $$n(n + 2) = 255$$.
Expanding the left side yields $$n^2 + 2n = 255$$.
Subtract $$255$$ from both sides to convert the quadratic equation into standard form: $$n^2 + 2n - 255 = 0$$.
Factor the trinomial to get $$(n - 15)(n + 17) = 0$$.
Setting each factor to zero using the Zero Product Property gives the solutions $$n = 15$$ and $$n = -17$$.

This results in two possible pairs of consecutive odd integers:
- For $$n = 15$$, the next odd integer is $$15 + 2 = 17$$.
- For $$n = -17$$, the next odd integer is $$-17 + 2 = -15$$.

The valid sets of consecutive odd integers are $$15$$ and $$17$$, and $$-17$$ and $$-15$$.

Solving for Two Consecutive Odd Integers Whose Product is $$255$$

Apply the problem-solving strategy to find two consecutive odd integers whose product is $$483$$.

Let $$n$$ represent the first odd integer, which means the next consecutive odd integer is $$n + 2$$.
The equation for their product is: $$n(n + 2) = 483$$.
Distribute $$n$$ to obtain $$n^2 + 2n = 483$$.
Convert the equation to standard quadratic form by subtracting $$483$$ from both sides: $$n^2 + 2n - 483 = 0$$.
Factor the resulting trinomial to find $$(n - 21)(n + 23) = 0$$.
Applying the Zero Product Property yields two possible values for the first integer: $$n = 21$$ and $$n = -23$$.

Thus, there are two valid pairs of consecutive odd integers:
- If $$n = 21$$, the next odd integer is $$21 + 2 = 23$$.
- If $$n = -23$$, the next odd integer is $$-23 + 2 = -21$$.

The pairs of consecutive odd integers are $$21$$ and $$23$$, and $$-23$$ and $$-21$$.

Solving for Two Consecutive Odd Integers Whose Product is $$483$$

Apply the seven-step problem-solving strategy to find an unknown past value based on a known present value and a comparative phrase.

**Problem:** Normal yearly snowfall at the local ski resort is $$12$$ inches more than twice the amount it received last season. The normal yearly snowfall is $$62$$ inches. What was the snowfall last season at the ski resort?

**Step 1. Read** the problem.
**Step 2. Identify** what you are looking for: What was the snowfall last season?
**Step 3. Name** what we are looking for and choose a variable to represent it: Let $$s$$ = the snowfall last season.
**Step 4. Translate.** Restate the problem in one sentence with all the important information: "The normal snowfall is $$62$$, which is $$12$$ more than twice the amount last year." Translate into an equation: $$62 = 2s + 12$$.
**Step 5. Solve** the equation.
Subtract $$12$$ from each side: $$62 - 12 = 2s + 12 - 12$$
Simplify: $$50 = 2s$$
Divide each side by two: $$\frac{50}{2} = \frac{2s}{2}$$
Simplify: $$25 = s$$
**Step 6. Check:** Is our answer reasonable? Yes, having $$25$$ inches of snow seems OK. The problem says the normal snowfall is twelve inches more than twice the number of last season. Twice $$25$$ is $$50$$ and $$12$$ more than that is $$62$$.
**Step 7. Answer** the question: The snowfall last season was $$25$$ inches.

Example: Solving a Word Problem about Snowfall

Apply the seven-step problem-solving strategy to a word problem involving a comparative relationship between two unknown quantities.

**Problem:** Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was three more than twice the number of notebooks. He bought seven textbooks. How many notebooks did he buy?

**Step 1. Read** the problem.
**Step 2. Identify** what you are looking for: How many notebooks did Guillermo buy?
**Step 3. Name** what we are looking for: Let $$n$$ = the number of notebooks.
**Step 4. Translate:** Restate the problem into an equation. The number of textbooks ($$7$$) was three more than twice the number of notebooks ($$2n + 3$$), which translates to: $$7 = 2n + 3$$.
**Step 5. Solve** the equation:
Subtract $$3$$ from both sides: $$4 = 2n$$
Divide by $$2$$: $$2 = n$$
**Step 6. Check:** If he bought $$2$$ notebooks, is three more than twice that equal to $$7$$? Twice $$2$$ is $$4$$, and $$4 + 3 = 7$$. The total matches the $$7$$ textbooks.
**Step 7. Answer:** Guillermo bought $$2$$ notebooks.

Example: Solving a Word Problem about Books

Apply the seven-step problem-solving strategy to a word problem involving solving for an unknown quantity derived from a "more than twice" relationship.

**Problem:** Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is eight more than twice the number of crossword puzzles. He completed $$22$$ Sudoku puzzles. How many crossword puzzles did he do?

**Step 1. Read** the problem.
**Step 2. Identify** what you are looking for: How many crossword puzzles did Gerry do?
**Step 3. Name** what we are looking for: Let $$c$$ = the number of crossword puzzles.
**Step 4. Translate:** Restate the problem into an equation. The number of Sudoku puzzles ($$22$$) is eight more than twice the number of crossword puzzles ($$2c + 8$$), which translates to: $$22 = 2c + 8$$.
**Step 5. Solve** the equation:
Subtract $$8$$ from both sides: $$14 = 2c$$
Divide by $$2$$: $$7 = c$$
**Step 6. Check:** If he completed $$7$$ crossword puzzles, is eight more than twice that equal to $$22$$? Twice $$7$$ is $$14$$, and $$14 + 8 = 22$$. The total matches the $$22$$ Sudoku puzzles.
**Step 7. Answer:** Gerry did $$7$$ crossword puzzles.

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