Solving a Punch Mixture Problem with a Known Total
Apply the seven-step problem-solving strategy to a mixture word problem involving a known total volume to find the amounts of two combined liquid ingredients.
Problem: Becca wants to mix fruit juice and soda to make a punch. She can buy fruit juice for $3 a gallon and soda for $4 a gallon. If she wants to make gallons of punch at a cost of $3.25 a gallon, how many gallons of fruit juice and how many gallons of soda should she buy?
- Read the problem: fruit juice (worth $3 per gallon) and soda (worth $4 per gallon). The total mixture is gallons at $3.25 per gallon.
- Identify what to find: the number of gallons of fruit juice and the number of gallons of soda.
- Name the unknowns using a single variable and the known-total technique. Let = the number of gallons of fruit juice. Then the number of gallons of soda is . Organize in a table:
| Type | Gallons | Price per gallon ($) | Total Value ($) |
|---|---|---|---|
| Fruit juice | |||
| Soda | |||
| Punch |
-
Translate into an equation. The value of the fruit juice plus the value of the soda equals the value of the punch:
-
Solve the equation:
- Distribute :
- Combine like terms:
- Subtract from both sides:
- Divide by : Find the number of gallons of soda: .
-
Check: ✓
-
Answer: Becca should buy gallons of fruit juice and gallons of soda.
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
Algebra
Related
A deli manager is mixing two types of gourmet coffee beans to create a 15-pound signature blend. If the manager uses 'x' pounds of the first type of bean, which expression represents the number of pounds of the second type of bean needed to complete the 15-pound mixture?
A production manager is preparing a 40-pound batch of a custom coffee blend. Match each component of the mixture problem to its correct mathematical description using the total-value model and the known-total technique, where 'x' represents the weight of the first coffee type.
A production supervisor is preparing a 500-pound batch of a specialized chemical sealant. If the weight of the first chemical component is represented by the variable , the 'known-total technique' correctly represents the weight of the second component as the expression $500 - c$.
A commercial kitchen manager is preparing a 20-pound batch of specialty trail mix for a corporate event. According to the seven-step problem-solving strategy, in what order should the manager perform these steps to determine the correct weight of each ingredient needed for the mixture?
Defining the Total-Value Model Formula
A warehouse supervisor is blending two types of bulk grain for a 500-pound wholesale order. When using the total-value model (number · value = total value) for this weight-based mixture, the 'value' component of the formula specifically represents the ____ of the grain.
Logistics and Inventory: Bulk Blending Strategy
Inventory Training: Applying the Total-Value Model to Bulk Mixtures
A landscaping supervisor is mixing two grades of mulch for a commercial project where the product is sold by weight. When applying the total-value model () to this mixture, what does the 'number' component specifically represent?
A production supervisor is training a new inventory clerk on the 'Translate' step of the seven-step strategy for solving mixture problems. According to this model, which mathematical relationship is used to form the equation for a two-ingredient mixture?
Solving a Party Mix Mixture Problem
Solving a Punch Mixture Problem with a Known Total