Chapter 7.2, Problem 82E

To determine

To find : the number of calories in cheeseburgers and French fries.

Answer to Problem 82E

The number of calories in cheeseburgers and French fries are $300\text{ calories}$ and $230\text{ calories}$ respectively.

Explanation of Solution

Given information :

Two cheeseburgers and one small order of French fries from a fast food restaurant contain a total of $830\text{ calories}$ . Three cheeseburgers and two small orders of French fries contain a total of $1360\text{ calories}\text{.}$

Calculation :

Let $x$ and $y$ denote the number of calories in cheeseburgers and French fries respectively.

According to the question

  $2x+y=830$  ...(1)

  $3x+2y=1360$  ...(2)

Multiply equation (1) by $2$ :

  $4x+2y=1660$  ...(3)

Solve equation (2) and (3) by elimination method:

  $\underset{\_}{\begin{array}{l}\text{ 4}x+2y=1660\\ \text{- 3}x+2y=1360\end{array}}$

  $\text{ x=300}$

Calculate value of $y$ by putting value of $x$ in equation (1):

  $\begin{array}{l}2\times 300+y=830\\ y=830-600\\ y=230\end{array}$

Therefore,the number of calories in cheeseburgers and French fries are $300\text{ calories}$ and $230\text{ calories}$ respectively.