Francie has $\$4.35$ in dimes and quarters. The number of dimes is five more than the number of quarters. How many of each coin does she have?

The number of dimes is five more than the number of quarters and Francie has $\$4.35$of quarters in dimes and quarters. We have to find the number of coins she has.

Let xbe the number of quarters.

Now, the number of dimes is five more than the number of quarters.

So, the number of dimes $=x+5$

The value of quarters in the dollar is $0.25$and the value of dimes in the dollar is $0.10.$

Thus, the table is

The total value of dimes and quarters is$\$4.35.$

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

So,$0.25x+0.10(x+5)=4.35$

By proceeding with the equation we get,

$$\begin{gathered} 0.25x+0.10(x+5)=4.35 \\ 0.25x+0.10x+0.5=4.35 \\ 0.35x+0.5=4.35 \\ 0.35x=4.35-0.5 \\ 0.35x=3.85 \\ x=\frac{3.85}{0.35} \\ x=11 \end{gathered}$$

So, there are $11$quarters and dimes $$\begin{gathered} =11+5 \\ =16 \end{gathered}$$

Francie has total $\$4.35$in dimes and quarters.

We have found that she has $11$quarters and $16$dimes.

$$\begin{gathered} 11\left(0.25\right)+16(0.10)=4.35 \\ 2.75+1.6=4.35 \\ 4.35=4.35 \end{gathered}$$

It is true.

Therefore, Francie has$11$quarters and$16$dimes.