Question

Jesse has $\$6.55$worth of quarters and nickels in his pocket. The number of nickels is five more than two times the number of quarters. How many nickels and how many quarters does Jesse have?

Short answer

Jesse has $18$quarters and$41$nickels.

Step-by-step solution

Step 1. Given information.

Consider the given question,

The number of nickels is five more than two times the number of quarters.

We know, the value of a nickels is $\$0.05$and value of quarters is $\$0.25$. The total value of all the coins is $\$6.55$.

Assume nand qto be the number of nickels and quarters. Then,

$n=5+2q$

Make the table,

Step 2. Form the equation.

Consider the table, we can see,

$$\begin{gathered} 0.05\left(5+2q\right)+0.25q=6.55 \\ 0.25+0.1q+0.25q=6.55 \\ 0.35q=6.3 \\ q=18 \end{gathered}$$

Then,

$$\begin{gathered} n=5+2\left(18\right) \\ n=5+36 \\ n=41 \end{gathered}$$

Therefore, Jesse has $41$nickels and $18$quarters in his pocket.