Question

A child's piggy bank contains 44 coins in quarters and dimes. The coins have a total value of $8.60. Findthe number of quarters in the bank.

Answer 1

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.

`q+d=44\quad \text{eq}.1`

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

`0.25q+0.10d=8.60\quad eq.2`

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

`\begin{gathered} q+d=44 \\ d=44-q\quad eq.1 \end{gathered}`

Now substitute this value into the eq.2

`\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=(4.2)/(0.15) \\ q=28 \end{gathered}`

Therefore, the number of quarters in the bank are 28

(dimes are 44 - 28 = 16)