Question

My math problem says at McDonald's four cheeseburgers and three medium fries have a total of 2290 calories. Six cheeseburgers and 2 medium fries have a total of 2560 calories. how many calories does each item have? I have defined the variables and I wrote a system already, but I'm not sure how to solve it.

Answer 1

In order to determine the number of calories for each item, it is necessary to write a system of equations.

If x is the number of calories cheeseburgers have and y the number of calories medium fries have, then, you have:

4x + 3y = 2290 (1)

6x + 2y = 2560 (2)

To solve the previous system, multiply the first equation by 2 and the second equation by 3:

2(4x + 3y = 2290)

8x + 6y = 4580 (3)

3(6x + 2y = 2560)

18x + 6y = 7680 (4)

next, subtract the last equation to the equation (3):

8x + 6y = 4580

-18x - 6y = -7680

-10x + 0 = -3100

from the previous result, solve for x:

-10x = -3100

x = 3100/10

x = 310

next, replace the value of x into the equation (1) and solve for y:

4x + 3y = 2290

4(310) + 3y = 2290

1240 + 3y = 2290

3y = 2290 - 1240

3y = 1050

y = 350

Hence, the number of calories of cheeseburgers is 310, and the number of calories of medium fries is 350.