Question

. Marco bought pens and pencils with his company's name and website address to give away to people at a festival. He bought a total of 300 pens and pencils together and spent $62.50. If pencils cost $0.15 each and pens cost $0.25 each, how many pens did Marco buy? A. 175 B. 165 C. 140 D. 130 E. 125

Answer 1

He bought a total of 300 pens and pencils and spend $62.50.

Each pen cost $0.25 and each pencil cost $0.15.

Lets call x the number of pens and y the number of pencils.

Then, as the sum of x and y is 300, we can write:

$x+y=300$

The total cost is $62.50, which is the result of adding each individual cost: the price multiplied by the quantity.

Then, we can write:

$0.25x+0.15y=62.50$

We use the information of the first equation to define y in function of x and replace in the second equation:

$x+y=300\longrightarrow y=300-x$$\begin{gathered} 0.25\cdot x+0.15\cdot(300-x)=62.50 \\ 0.25x+45-0.15x=62.50 \\ 0.10x=62.50-45 \\ 0.10x=17.5 \\ x=\frac{17.5}{0.10} \\ x=175 \end{gathered}$

Knowing x, we can calculate y:

$y=300-x=300-175=125$

He bought 125 pencils and 175 pens.

Answer: A. 175