Question

Michaela has $\$2.05$in dimes and nickels in her change purse. She has seven more dimes than nickels. How many coins of each type does she have?

Short answer

Michaela has $9$nickels and $16$dimes in her purse.

Step-by-step solution

Step 1. Given information.

Consider the given question,

Michaela has seven more dimes than nickels.

We know, the value of a dime is $\$0.1$and value of nickel is $\$0.05$. The total value of all the coins is $\$2.05$.

Assume nand dto be the number of nickels and dimes.

localid="1647107421767" $d=n+7$

Make the table,

Step 2. Form the equation.

Consider the table, we can see,

$$\begin{gathered} 0.1\left(n+7\right)+0.05n=2.05 \\ 0.1n+0.7+0.05n=2.05 \\ 0.15n=1.35 \\ n=9 \end{gathered}$$

Then,

$$\begin{gathered} d=9+7 \\ d=16 \end{gathered}$$

Therefore, the number of nickels is $9$and the number of dimes is $16$.