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.

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.