Question

Jamey has $4$ quarters, some dimes, and some pennies. If the ratio of quarters to dimes is $8:6$ and the ratio of pennies to dimes is $7:3$, then how many pennies does Jamey have?

Answer 1

Step-1: Find number of dimes:

Let the number of dimes and pennies be $x$ and $y$ respectively.

Given ratio of quarter and dines is $8:6$.

There are $4$ quarters.

So, we have $4:x::8:6$.

Then we will solve proportion $4:x::8:6$ to find $x$.

$\begin{array}{rcl}\frac{4}{x}& =& \frac{8}{6}\\ & \Rightarrow & 4\times 6=8\times x\left(\mathrm{Cross}\mathrm{multiplying}\mathrm{both}\mathrm{sides}\right)\\ \Rightarrow 24& =& 8x\\ \Rightarrow \frac{24}{8}& =& x\left(\mathrm{Dividing}\mathrm{both}\mathrm{sides}\mathrm{by}8\right)\\ \Rightarrow 3& =& x\\ \therefore x& =& 3\end{array}$

Therefore, there are $3$ dimes.

Step-2: Find number of pennies:

The ratio of pennies to dimes is $7:3$.

There are $y$ pennies and $3$ dimes.

So, we have $y:3::7:3$.

Solving proportion $y:3::7:3$, to find $y$.

$$\begin{gathered} \frac{y}{3}=\frac{7}{3} \\ \Rightarrow y=\frac{7}{3}·3\left(\mathrm{Multiplying}\mathrm{both}\mathrm{sides}\mathrm{by}3\right) \\ \therefore y=7 \end{gathered}$$

Therefore the number of pennies is $7$.

Hence, the number of pennies James have is $7$.