Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Two coworkers picked up some writing instruments at the office supply store. Francesca selected 6 boxes of pencils and 9 boxes of ballpoint pens, paying $30. Next, Terrence spent $18 on 7 boxes of pencils and 2 boxes of ballpoint pens. How much does a box of each cost?

Answer 1

Given that:

- Francesca spent $30 on 6 boxes of pencils and 9 boxes of ballpoint pens.

- Terrence spent $18 on 7 boxes of pencils and 2 boxes of ballpoint pens.

Let be "p" the cost (in dollars) of a box of pencils and "b" the cost (in dollars) of a box of ballpoint pens.

You can write the following equation to represent the total cost (in dollars) of 6 boxes of pencils and 9 boxes:

`6p+9b=30`

And you can write the second equation to represent the total cost (in dollars) of 7 boxes of pencils and 2 boxes of ballpoint pens:

`7p+2b=18`

Having these equations, you can set up the following System of Equations to describe the situation given in the exercise:

`\begin{cases}6p+9b=30 \\ \\ 7p+2b=18\end{cases}`

In order to solve it, you can use the Elimination Method:

1. Multiply the first equation by 7 and the second equation by -6:

`\begin{cases}42p+63b=210 \\ \\ -42p-12b=-108\end{cases}`

2. Add the equations:

`\begin{gathered} \begin{cases}42p+63b=210 \\ \\ -42p-12b=-108\end{cases} \\ -------------- \\ 0+51b=102 \\ 51b=102 \end{gathered}`

3. Solve for "b":

`\begin{gathered} b=(102)/(51) \\ \\ b=2 \end{gathered}`

4. Substitute the value of "b" into one of the original equations:

`\begin{gathered} 7p+2b=18 \\ 7p+2(2)=18 \end{gathered}`

5. Solve for "p":

`\begin{gathered} 7p+4=18 \\ 7p=18-4 \\ \\ p=(14)/(7) \\ \\ p=2 \end{gathered}`

Hence, the answer is:

- Cost of a box of pencils: $2.00

- Cost of a box of ballpoint pens: $2.00