1Cademy - Solving a Calorie-Counting Word Problem Using a System of Equations by Elimination

Learn Before

Problem-Solving Strategy for Systems of Linear Equations

Example

Solving a Calorie-Counting Word Problem Using a System of Equations by Elimination

Apply the seven-step problem-solving strategy for systems of linear equations to a real-world calorie-counting problem, using elimination to solve the resulting system.

Problem: Joe stops at a burger restaurant every day on his way to work. Monday he had one order of medium fries and two small sodas, which had a total of 620 calories. Tuesday he had two orders of medium fries and one small soda, for a total of 820 calories. How many calories are there in one order of medium fries? How many calories in one small soda?

Read the problem.
Identify what to find: the number of calories in one order of medium fries and in one small soda.
Name the unknowns: Let $f$ = the number of calories in one order of medium fries. Let $s$ = the number of calories in one small soda.
Translate into a system of equations. Monday's order gives $f + 2s = 620$ . Tuesday's order gives $2f + s = 820$ . The system is:

$\left\{\begin{array}{l} f + 2s = 620 \\ 2f + s = 820 \end{array}\right.$

Solve using elimination. Both equations are in standard form. To create opposite coefficients of $f$ , multiply the first equation by $-2$ :

$-2(f + 2s) = -2(620) \implies -2f - 4s = -1240$

Add this to the second equation:

$-2f - 4s + 2f + s = -1240 + 820$

$-3s = -420$

Divide both sides by $-3$ : $s = 140$ .

Substitute $s = 140$ into the first equation:

$f + 2(140) = 620$

$f + 280 = 620$

$f = 340$

Check: Monday: $340 + 2(140) = 340 + 280 = 620$ ✓. Tuesday: $2(340) + 140 = 680 + 140 = 820$ ✓.
Answer: One small soda has 140 calories and one order of medium fries has 340 calories.

This example shows how a real-world scenario involving two different combinations of the same items naturally produces a system of equations in standard form, making elimination a convenient solving method. Each day's order translates directly into one equation — the coefficients represent the quantities ordered and the constant represents the total calorie count. Unlike the sum-and-difference number problem — where the coefficients are already opposites and the equations can be added immediately — this system requires multiplying the first equation by $-2$ before adding, because the original coefficients of $f$ ( $1$ and $2$ ) are not yet opposites.

Updated 2026-04-21

Contributors are:

Who are from:

References

Learn Before

Related

Learn After