Question

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?

Answer 1

There are 230 calories in each cheeseburger and 290 calories in each small fries.

Explanation:

Let us assume:

The calories in each cheeseburger = x

The calories in each small fries = y

So, the calories in 4 cheeseburger

=4 (calories in 1 cheeseburger ) = 4 x

and the calories in 5 small fries = 5(calories in 1 small fries ) =5 y

⇒ 4 x + 5 y = 2310

Similarly, calories in 3 cheeseburger

= 3 ( calories in 1 cheeseburger ) = 3 x

and the calories in 2 small fries = 2 (calories in 1 small fries )= 2 y

⇒ 3 x + 2 y = 1330

Solving the given system of equation:

4 x + 5 y = 2310 ............(1)

3 x + 2 y = 1330 ............. (2)

Multiply equation (1) with (-3) , and (2) by 4 and add both equation.

-12 x - 15 y + 12 x + 8 y = -6930 + 5320

or, - 7 y = -1610

⇒ y = 1610 / 7 = 230 , or y = 230

Putting this in (2) , we get 3 x + 2 y = 1330

⇒ 3 x + 2(230) = 1330 or, 3 x = 1330 - 460 = 870

or, x = 870/3 = 290

⇒ x = 290

Hence, there are 230 calories in each cheeseburger.

There are 290 calories in each small fries.