Respuesta :
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:
[tex]6p+9b=30[/tex]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:
[tex]7p+2b=18[/tex]Having these equations, you can set up the following System of Equations to describe the situation given in the exercise:
[tex]\begin{cases}6p+9b=30 \\ \\ 7p+2b=18\end{cases}[/tex]In order to solve it, you can use the Elimination Method:
1. Multiply the first equation by 7 and the second equation by -6:
[tex]\begin{cases}42p+63b=210 \\ \\ -42p-12b=-108\end{cases}[/tex]2. Add the equations:
[tex]\begin{gathered} \begin{cases}42p+63b=210 \\ \\ -42p-12b=-108\end{cases} \\ -------------- \\ 0+51b=102 \\ 51b=102 \end{gathered}[/tex]3. Solve for "b":
[tex]\begin{gathered} b=\frac{102}{51} \\ \\ b=2 \end{gathered}[/tex]4. Substitute the value of "b" into one of the original equations:
[tex]\begin{gathered} 7p+2b=18 \\ 7p+2(2)=18 \end{gathered}[/tex]5. Solve for "p":
[tex]\begin{gathered} 7p+4=18 \\ 7p=18-4 \\ \\ p=\frac{14}{7} \\ \\ p=2 \end{gathered}[/tex]Hence, the answer is:
- Cost of a box of pencils: $2.00
- Cost of a box of ballpoint pens: $2.00
