Chapter 6.2, Problem 34PPE

To determine

To find the number of dimes and quarters if total value is $3.70 and number of quarters is 5 more than the number of dimes.

Answer to Problem 34PPE

7 dimes and 12 quarters.

Explanation of Solution

Given information:

Total value of the coins is $3.70 and number of quarters is 5 more than the number of dimes.

Concept used:

  $\begin{array}{l}1\text{dime}=0.1\text{dollar}\\ 1\text{quarter}=0.25\text{dollar}\end{array}$

Calculation:

Let the number of dimes be $x$ , then the number of quarters is $x+5$ .

Now given that the total value of the coins is $3.70. That is,

  $\begin{array}{l}0.1x+0.25\left(x+5\right)=3.70\\ \Rightarrow 0.1x+0.25x+1.25=3.70\\ \Rightarrow 0.35x=2.45\\ \Rightarrow x=7\end{array}$

Therefore,

  $\begin{array}{l}\text{Number}\text{of}\text{dimes}=x=7\\ \text{Number}\text{of}\text{quarters}=x+5=7+5=12\end{array}$