Question

The cost of a pen is three times the cost of a pencil. The cost of 4 pencils and 3 pens is $9.75. What is the cost of a pencil?

Answer 1

`\$0.75`

Step-by-step explanation

Let the cost of the pen be x.

Let the cost of the pencil be y.

The pen costs 3 times as much as the pencil. This implies that:

`x=3y`

The cost of 4 pencils and 3 pens is $9.75. This implies that:

`4y+3x=9.75`

Substitute the first equation into the second equation:

`4y+3(3y)=9.75`

Simplify and solve for y:

`\begin{gathered} 4y+9y=9.75 \\ 13y=9.75 \\ \Rightarrow y=(9.75)/(13) \\ y=\$0.75 \end{gathered}`

That is the cost of a pencil.