Chapter 6.2, Problem 17P

A student bought 1 box of crayons and 5 reams of paper for $54. She bought 5 boxes of crayons and 3 reams of paper for $50. What is the cost of each box of crayons and each ream of paper?

To determine

To find: The cost of each box of crayons and each ream of paper with given conditions.

Answer to Problem 17P

The cost of each box of crayons is $4 and the cost of each ream of paper is $10.

Explanation of Solution

Given information:

The cost of each box of crayons and each ream of paper when a student bought 1 box of crayon and 5 reams of paper is $54. She bought 5 box of crayons and 3 reams of paper for $50.

Calculation:

Let us assume the cost of each box of crayons is x and the cost of each ream of paper is y. Hence we can write the above statement in equation form as follows:

  $\begin{array}{l}x+5y=54\\ 5x+3y=50\end{array}$

In order to solve two systems by substitution, we solve one of the equations for one of the variables, and plug this into other equation.

  $\begin{array}{l}x+5y=54\\ 5x+3y=50\end{array}$

As it is given that

  $\begin{array}{l}x+5y=54\\ \Rightarrow x=54-5y\end{array}$

Now we substitute $x=54-5y$ into $5x+3y=50$ , we get,

  $\begin{array}{l}5x+3y=50\\ \Rightarrow 5(54-5y)+3y=50\\ \Rightarrow 270-25y+3y=50\\ \Rightarrow -22y=-220\\ \Rightarrow y=10\end{array}$

By plugging $y=10$ in equation $x=54-5y$ we get

  $\begin{array}{l}x=54-5y\\ \Rightarrow x=54-5\times 10\\ \Rightarrow x=4\end{array}$

Therefore the solution is

  $\left(x,y\right)=(4,10)$

The cost of each box of crayons is $4 and the cost of each ream of paper is $10.