Respuesta :
Hello!
First of all, let's write some important information:
• There are 35 coins in total;
,• The total amount is $6.80.
Let's write d for dimes and q for quarters.
Writing the exercise as a linear system, we will have:
[tex]\begin{cases}d+q={35} \\ 0.10d+0.25q={6.80}\end{cases}[/tex]Let's isolate the variable d in the first equation:
[tex]\begin{cases}d+q={35\rightarrow d=35-q} \\ 0.10d+0.25q={6.80}\end{cases}[/tex]Now let's replace it in the second equation:
[tex]\begin{gathered} 0.10d+0.25q=6.80 \\ 0.10(35-q)+0.25q=6.80 \\ 3.50-0.10q+0.25q=6.80 \\ 0.15q=6.80-3.50 \\ 0.15q=3.30 \\ q=\frac{3.30}{0.15} \\ \\ \boxed{q=22\text{ quarter coins}} \end{gathered}[/tex]As we know the number of quarters, we just have to replace it:
[tex]\begin{gathered} d+q=35 \\ d+22=35 \\ d=35-22 \\ \boxed{d=13\text{ dimes coins}} \end{gathered}[/tex]Answer:
In the pig bank were 13 dimes coins and 22 quarter coins.
