Question

Chi has $\$11.30$in dimes and quarters. The number of dimes is three more than three times the number of quarters. How many of each are there?

Short answer

The number of quarters is$20$and number of dimes is$63$.

Step-by-step solution

Step 1. Given Information

Total Amount $=\$11.30$

Number of dimes is three more than three times the number of quarters.

Step 2. Naming the variables

Let the number of quarters be $x$.

We know, number of dimes = $3\times$number of quarters $+3$

Therefore, number of dimes$=3x+3$

Step 3. Creating the table

The required table is

Step 4. Solving the equation

Translating into equation we get,

$$\begin{gathered} 0.25x+0.10(3x+3)=11.30 \\ \Rightarrow 0.25x+0.30x+0.30=11.30 \\ \Rightarrow 0.55x=11.30-0.30 \\ \Rightarrow 0.55x=11 \\ \Rightarrow x=\frac{11}{0.55} \\ \Rightarrow x=20 \\ \therefore 3x+3=3\left(20\right)+3 \\ \Rightarrow 3x+3=60+3 \\ \Rightarrow 3x+x=63 \end{gathered}$$