Chapter 6.5, Problem 6STP

A school fundraiser sells holiday cards and wrapping paper. They are trying to raise at least $400. They make a profit of $1.50 on each box of holiday cards and $1.00 on each pack of wrapping paper.

a. What is an inequality for the profit the school wants to make for the fundraiser?

b. If the fundraiser sells 100 boxes of cards and 160 packs of wrapping paper, will they reach their goal? Show your work.

To determine

To find: the inequality for the profit that the school wants to make for the fundraiser

Answer to Problem 6STP

Inequality is $1.50x+y\ge 400$

Explanation of Solution

Given information: A school fundraiser is trying to raise at least $\$400$ by selling holiday cards and wrapping paper. A profit of $\$1.50$ is made on each box of holiday cards and profit of $\$1.00$ is made on each pack of wrapping paper.

Let $x$ denotes number of boxes of holiday cards and $y$ denotes number of packs of wrapping paper.

Profit made from selling 1 box of holiday cards $=\$1.50$

Profit made from selling $x$ boxes of holiday cards $=\$1.50x$

Profit made from selling 1 pack of wrapping paper $=\$1.00$

Profit made from selling $y$ boxes of holiday cards $=\$1y=\$y$

So,

Total profit made from selling holiday cards and wrapping paper $=\$1.50x+\$y$

As school fundraiser is trying to raise at least $\$400$ by selling holiday cards and wrapping paper, inequality is $1.50x+y\ge 400$

To determine

To verify: whether the fundraiser will reach the goal if 100 boxes of cards and 160 packs of wrapping papers are sold

Explanation of Solution

Calculation:

Inequality that must be satisfied so that the fundraiser reaches the goal is $1.50x+y\ge 400$

Number of boxes of cards sold $(x)=100$

Number of packs of wrapping papers sold $(y)=160$

Put $x=100,y=160$ in $1.50x+y\ge 400$

  $\begin{array}{l}1.50(100)+160\ge 400\\ 150+160\ge 400\end{array}$

  $310\ge 400$ which is not true.

So, $x=100,y=160$ does not satisfy the equation $1.50x+y\ge 400$

Therefore, fundraiser will not reach the goal if 100 boxes of cards and 160 packs of wrapping papers are sold