Chapter 12.4, Problem 42STP

To determine

To find: the number of quarters that the person has.

Answer to Problem 42STP

The person can have C-18 quarters.

Explanation of Solution

Given information:

The person has 30 coins, quarters and dimes. Their total cost is $5.70.

Given options-

A − 12, B − 15, C − 18, D − 20.

Calculation:

Here, we have to find the number of quarters that the person has.

Note that,

  $\begin{array}{l}1\text{ quarter}=\$0.25\\ 1\text{ dime}=\$0.10\end{array}$

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

Total coins are 30.

So, $x+y=\mathrm{30.......}\left(i\right)$

Total amount is $5.70.

So, $0.25x+0.10y=\mathrm{5.70.......}\left(ii\right)$

Solve for $x$ , that is, quarters

  $x+y=30$

Put the value of $x+y=30$ in equation $\left(ii\right)$

  $\begin{array}{l}0.25x+0.10\left(30-x\right)=5.70\\ 0.25x+3-0.10x=5.70\\ 0.15x=5.70-3\\ 0.15x=2.70\\ x=\frac{2.70}{0.15}\\ x=18\end{array}$

Hence, the person can have 18 quarters.