Question

Ngo has a collection of dimes and quarters with a total value of $\$3.50$. The number of dimes is seven more than the number of quarters. How many of each coin does he have?

Short answer

The number of dimes are $15$ and the quarters are$8$

Step-by-step solution

Step 1. Given Information

Total amount of money$=\$3.50$

Let he number of quarters be $x$

Therefore ,

According to the question,

number of dimes will be$x+7$

Step 2. Solution of the equation 

Now, According to the question,

$$\begin{gathered} 0.25x+0.10(x+7)=3.50 \\ 0.25x+0.10x+0.7=3.50 \\ 0.35x+0.7-0.7=3.50-0.7 \\ 0.35x=2.8 \\ x=8 \\ x+7=8+7=15 \end{gathered}$$