Question

In the following exercises, translate to a system of equations and solve. Lucinda had a pocketful of dimes and quarters with a value of $ 6.20. The number of dimes is eighteen more than three times the number of quarters. How many dimes and how many quarters does Lucinda have?

Short answer

The number of quarters are 8 and number of dimes are 42.

Step-by-step solution

Step 1. Given Information  

The given data is that Lucinda had a pocketful of dimes and quarters with a value of $ 6.20. The number of dimes is eighteen more than three times the number of quarters.

Step 2. Calculation   

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

Total number of quarters and dimes is $\$6.20$. Quarter has one-fourth of the value and one dime has one tenth value that can be shown as$\frac{1}{4}x+\frac{1}{10}y=6.20--\left(1\right)$

The number of dimes is eighteen more than three times the number of quarters that is$y=3x+18--\left(2\right)$

Substitute the value of y from equation (2) in equation (1) to find the value of x.

$$\begin{gathered} \frac{1}{4}x+\frac{1}{10}(3x+18)=6.20 \\ 0.25x+0.3x+1.8=6.20 \\ x=\frac{6.20-1.8}{0.55} \\ x=8 \end{gathered}$$

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

$$\begin{gathered} y=3\left(8\right)+18 \\ y=24+18 \\ y=42 \end{gathered}$$