Question

Translate to a system of equations and solve:

Matilda has a handful of quarters and dimes, with a total value of $8.55. The number of quarters is 3 more than twice the number of dimes. How many dimes and how many quarters does she have?

Short answer

The number of quarter are 29 and number of dimes are 13.

Step-by-step solution

Step 1. Given Information  

The given data is that Matilda has a handful of quarters and dimes, with a total value of $8.55. The number of quarters is 3 more than twice the number of dimes.

Step 2. Calculation  

Let the number of quarters be x and the number of dimes be y.

Quarter is one-fourth of the value and one dime has one tenth value.

The total number of quarter and dimes is $\$8.55$that is $\frac{1}{4}x+\frac{1}{10}y=8.55--\left(1\right)$

The number of quarters is 3 more than twice the number of dimes that is $x=2y+3--\left(2\right)$

Substitute equation (2) in equation (1) and solve for y.

$$\begin{gathered} \frac{1}{4}(2y+3)+\frac{1}{10}y=8.55 \\ \frac{y}{2}+\frac{3}{4}+\frac{y}{10}=8.55 \\ \frac{5y+y}{10}=8.55-0.75 \\ \frac{6y}{10}=7.8 \\ y=13 \end{gathered}$$

Substitute the value of y in equation (2) to find the value of x.

$$\begin{gathered} x=2\left(13\right)+3 \\ x=26+3 \\ x=29 \end{gathered}$$