We are given the following information
A child's piggy bank contains 44 coins in quarters and dimes.
Let q represents the number of quarters.
Let d represents the number of dimes.
Then the sum of q and d must be 44 coins.
[tex]q+d=44\quad \text{eq}.1[/tex]The coins have a total value of $8.60
We know that the worth of a quarter is 0.25 cents and the worth of a dime is 0.10 cents
[tex]0.25q+0.10d=8.60\quad eq.2[/tex]Now we have 2 equations and 2 unknowns so we can easily solve these equations using the substitution method.
From eq. 1 separate the value of d
[tex]\begin{gathered} q+d=44 \\ d=44-q\quad eq.1 \end{gathered}[/tex]Now substitute this value into the eq.2
[tex]\begin{gathered} 0.25q+0.10d=8.60\quad eq.2 \\ 0.25q+0.10(44-q)=8.60 \\ 0.25q+4.4-0.10q=8.60 \\ 0.25q-0.10q=8.60-4.4 \\ 0.15q=4.2 \\ q=\frac{4.2}{0.15} \\ q=28 \end{gathered}[/tex]Therefore, the number of quarters in the bank are 28
(dimes are 44 - 28 = 16)
