Given the expression
[tex]0.1\cdot d+0.25\cdot q=12.5[/tex]Where
d = number of dimes
q = number of quarters
Given that there are 10 quarters, find the number of dimes.
To find it, substitute q by 10.
[tex]\begin{gathered} 0.1\cdot d+0.25\cdot10=12.5 \\ 0.1\cdot d+2.5=12.5 \end{gathered}[/tex]To isolate d, subtract 2.5 from each side:
[tex]\begin{gathered} 0.1\cdot d+2.5-2.5-12.5-2.5 \\ 0.1d=10 \end{gathered}[/tex]Finally, divide both sides by 0.1:
[tex]\begin{gathered} \frac{0.1\cdot d}{0.1}=\frac{10}{0.1} \\ d=10\cdot10 \\ d=100 \end{gathered}[/tex]Answer: There are 100 dimes.
