Question

Carolyn has $$2.55$ in her purse in nickels and dimes. The number of nickels is nine less than three times the number of dimes. Find the number of each type of coin.

Short answer

The number of dime is $12$ and number of nickel is$27$

Step-by-step solution

Step 1. Given Information

Total amount$=\$2.55$

There are two types of Money that is nickels and dimes.

Let he number of dimes be $x$

Therefore ,

According to the question,

number of nickels will be $3x-9$

Value of each dime$0.10$

The total value of dimes will be$0.10x$

Value of each nickel is$0.05$

Therefore, total value of nickels will be$0.05(3x-9)$

Step 2. Solution of the equation 

Now, According to the question,

$$\begin{gathered} 0.10x+0.05(3x-9)=2.55 \\ 0.10x+0.15x-0.45=2.55 \\ 0.25x-0.45=2.55 \\ 0.25x=2.55+0.45 \\ 0.25x=3 \\ x=12 \\ Therefore, \\ 3x-9=3\times 12-9 \\ =36-9 \\ =27 \end{gathered}$$