Lenny has $\$3.69$ in pennies, dimes, and quarters. The number of pennies is three more than the number of dimes. The number of quarters is twice the number of dimes. How many of each coin does he have?

The number of pennies is three more than the number of dimes and the number of quarters is twice the number of dimes. Lenny has $\$3.69$ in pennies, dimes, and quarters. We have to find the number of each coin he has.

Let xbe the number of dimes.

Now, the number of pennies is three more than the number of dimes.

So, the number of pennies $=x+3$

Now, the number of quarters is twice the number of dimes.

So, the number is $=2x$

Thus, the table is

The total value of pennies, dimes, and quarters are$\$3.69.$

Write the equation by adding the total value of all the types of coins.

So,$0.10\left(x\right)+0.01\left(x+3\right)+0.25\left(2x\right)=3.69$

By proceeding with the equation we get,

$$\begin{gathered} 0.10\left(x\right)+0.01\left(x+3\right)+0.25\left(2x\right)=3.69 \\ 0.10x+0.01x+0.03+0.5x=3.69 \\ 0.61x=3.69-0.03 \\ 0.61x=3.66 \\ x=6 \end{gathered}$$

Thus, the number of dimes is $6$, the number of pennies is$6+3=9,$and the number of quarters is$2\left(6\right)=12.$

To check the answer replacexby $6$into the original equation.

$$\begin{gathered} 0.10\left(6\right)+0.01\left(6+3\right)+0.25\left(2\left(6\right)\right)=3.69 \\ 0.6+0.09+0.25\left(12\right)=3.69 \\ 0.69+3=3.69 \\ 3.69=3.69 \end{gathered}$$

It is true.

Thus, the number of coins of dimes is$6,$the number of pennies is$9$, and the number of quarters is$12.$