Question

You have 63 coins in your piggy bank, all quarters and nickels. The total amount is $12.55. How many quarters do you have?

Answer 1

Let x be the number of quarters and y be the number of nickels in the piggy bank;

Since there are 63 coins in the piggy bank, then we have;

`x+y=63\ldots\ldots\ldots\text{.. equation 1}`

Also, 20nickels is 1 dollar and also 4 quarters is 1 dollar.

Since there is $12.55 in the piggy bank, we have;

`(1)/(4)x+(1)/(20)y=12.55\ldots\ldots\ldots\ldots\text{.equation 2}`
`\begin{gathered} \text{From equation 1;} \\ y=63-x\ldots\ldots\ldots\ldots\text{equation 3} \end{gathered}`

Then, we substitute equation 3 in equation 2, we have;

`\begin{gathered} (1)/(4)x+(1)/(20)(63-x)=12.55 \\ \text{Multiply through by 20} \\ 5x+63-x=251 \\ 4x=251-63 \\ 4x=188 \\ x=(188)/(4) \\ x=47 \end{gathered}`

Hence, the number of quarters in the piggy bank is 47