Question

Alison has three times as many dimes as quarters in her purse. She has $\$9.35$altogether. How many coins of each type does she have?

Short answer

Alison has $17$quarters and $51$dimes in her purse.

Step-by-step solution

Step 1. Given information.

Consider the given question,

Alison has three times as many dimes as quarters in her purse.

We know, the value of a dime is $\$0.1$and value of quarter is $\$0.25$. The total value of all the coins is $\$9.35$.

Assume nand dto be the number of nickels and dimes.

localid="1647163959363" $d=3q$

Make the table,

Step 2. Form the equation.

Consider the table, we can see,

$$\begin{gathered} 3q\left(0.1\right)+0.25q=9.35 \\ 0.3q+0.25q=9.35 \\ 0.55q=9.35 \\ q=17 \end{gathered}$$

Then,

$$\begin{gathered} =3\times 17 \\ =51 \end{gathered}$$

Therefore, Alison has $17$quarters and$51$dimes in her purse.