At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two small fries have a total of 1,330 calories. How many calories does each item contain? Create two equations to model this situation using X and Y for your variables. Use a comma to separate your equations.

Question

03-10-2017
Mathematics

contestada

At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two small fries have a total of 1,330 calories. How many calories does each item contain? Create two equations to model this situation using X and Y for your variables. Use a comma to separate your equations.

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Аноним Аноним · Answer 1 · 2017-10-03T14:08:49+02:00

Let x = calories in a cheeseburger
Let y = calories in an order of small fries

Four cheeseburgers and five small fries have 2,310 calories. Therefore
4x + 5y = 2310 (1)

Three cheeseburgers and two small fries have 1,330 calories. Therefore
3x + 2y = 1330 (2)

Equations (1) and (2) model the given situation.

To solve, multiply (1) by 2, and multiply (2) by 5 to obtain
8x + 10y = 4620 (3)
15x + 10y = 6650 (4)

Subtract (3) from (4).
7x = 2030
x = 290
From (1), obtain
5y = 2310 - 4*290 = 1150
y = 230

Answer:
The two equations are
4x + 5y = 2310
3x + 2y = 1330

The solutions are x = 290, y = 230.