Question

Steve only puts dimes and quarters into his piggy bank. Right now he has five more dimes than quarters there, and they make $\$74.35$. How many quarters and how many dimes are there in Steve's piggy bank?

Answer 1

Step-1: Formation of equation:

Let the number of quarters in the piggy bank be $x$

And the number of dimes in the piggy bank be $y$

According to the equation,

As Steve has five more dimes than quarters

$y=x+5$ …(1)

Given that total money in the piggy bank is $\$74.35$

Also, dimes are one-tenth of a dollar

and quarter are one-fourth of a dollar

This implies $\frac{1}{4}x+\frac{1}{10}y=74.35$ …(2)

Step-2: Find the number of dimes and quarter:

$\frac{1}{4}x+\frac{1}{10}y=74.35$

$\begin{array}{rcl}& \Rightarrow & \frac{5x+2y}{20}=74.35\left[\mathrm{Take}\mathrm{LCM}\hspace{0.17em}\mathrm{of}4\mathrm{and}10\right]\\ \Rightarrow 5x+2y& =& 20\times 74.35\left[\mathrm{Multiply}20\mathrm{both}\mathrm{sides}\right]\\ \Rightarrow 5x+2y& =& 1487\end{array}$

Put Equation(1) in Equation(2)

$\begin{array}{rcl}5x+2\left(x+5\right)& =& 1487\\ & \Rightarrow & 5x+2x+10=1487\\ \Rightarrow 7x& =& 1487-10\left[\mathrm{Subtract}10\mathrm{from}\mathrm{both}\mathrm{sides}\right]\\ \Rightarrow 7x& =& 1477\\ \Rightarrow x& =& \frac{1477}{7}\left[\mathrm{Divide}\mathrm{by}7\mathrm{both}\mathrm{sides}\right]\\ \Rightarrow x& =& 211\end{array}$

Put the value of $x$ it in equation(1)

$$\begin{gathered} y=211+5 \\ y=216 \end{gathered}$$

Hence, number of dimes are $216$ and number of quarters are $211.$