Question

A man ordered 5 times as many boxes of ballpoint pens as boxes of felt-tip pens. Ballpoint pens cost $4.33 per box, and felt-tip pens cost $3.43. If the man's order ofpens totaled $75.24, how many boxes of each type of pen did he buy?How many boxes of felt-tip pens did he buy?How many boxes of ballpoint pens did he buy?

Answer 1

3 boxes of felt-tip pens

15 boxes of ballpoint pens

Explanation:

Let x boxes of ballpoint pens and y boxes of felt-tip pens. With the help of the statement we formulate the following equations:

`\begin{gathered} x=5y\text{ (1)} \\ 4.33x+3.43y=75.24\text{ (2)} \end{gathered}`

We substitute equation (1) in equation (2) and solve for y, like this:

`\begin{gathered} 4.33\cdot5y+3.43y=75.24 \\ 21.65y+3.43y=75.24 \\ 25.08y=75.24 \\ y=(75.24)/(25.08) \\ y=3 \\ \\ \text{ Now, for x},\text{ replacing in (1)} \\ x=5\cdot3 \\ x=15 \end{gathered}`

Therefore, he bought 15 boxes of ballpoint pens and 3 boxes of felt-tip pens.