Question

Elane has $\$7.00$total in dimes and nickels in her coin jar. The number of dimes that Elane has is seven less than three times the number of nickels. How many of each coin does Elane have?

Short answer

Elane has$22$nickels and$59$dimes.

Step-by-step solution

Step 1. Given information.

Consider the given question,

The number of dimes that Elane has is seven less than three times the number of 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 $\$7.00$.

Assume nand dto be the number of nickels and dimes.

$d=3n-7$

Make the table,

Step 2. Form the equation.

Consider the table, we can see,

$$\begin{gathered} 0.05n+0.1\left(3n-7\right)=7 \\ 0.05n+0.3n-0.7=7 \\ 0.35n=7.7 \\ n=22 \end{gathered}$$

Then,

role="math" localid="1647167061393" $$\begin{gathered} d=3\left(22\right)-7 \\ d=66-7 \\ d=59 \end{gathered}$$

Therefore, Elane has $22$nickels and $59$dimes.