Chapter 7.2, Problem 43E

To determine

The solution of airspeed of the plane and speed of the wind.

Answer to Problem 43E

  $300$ Calories in a cheeseburger.

  $230$ Calories in a small order of French fries.

Explanation of Solution

Given information:

Two cheeseburgers and one small order of French fries from a fast-food restaurant contain a total of $830$ calories. Three cheeseburgers and two small orders of French fries contain a total of $1360$ calories. Find the caloric content of each item.

Calculation:

Let calories in a cheeseburger $=x$

Let calories in a small order of French fries $=y$

According to the given the equations are as shown below:

  $\begin{array}{l}2x+y=830\\ 3x+2y=1360\end{array}$

Multiply the first equation by $-2$ to produce coefficients of $y$ that differ only in sign:

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

Add the above equation together, cancelling out the $y$ variable:

  $\begin{array}{l}-x=-300\\ x=300\end{array}$

Substitute the value of $x$ into the first equation and solve for $y$ :

  $\begin{array}{l}2x+y=830\\ 2(300)+y=830\\ 600+y=830\\ y=230\end{array}$

There are $300$ calories in a cheeseburger and $230$ calories in a small order of French fries.