Question

Julio has $$2.75$ in his pocket in nickels and dimes. The number of dimes is 10 less than twice the number of nickels. Find the number of each type of coin.

Short answer

The number of nickels is $15$ and number of dimes is$20$

Step-by-step solution

Step 1. Given Information

Total amount$=\$2.75$

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

Let he number of nickels be$x$

Therefore ,

According to the question,

number of dimes will be $2x-10$

Value of each dime$0.10$

The total value of dimes will be$0.10(2x-10)$

Value of each nickel is$0.05$

Therefore, total value of nickels will be$0.05x$

Step 2. Solution of the equation  

Now, According to the question,

$$\begin{gathered} 0.10(2x-10)+0.05x=2.75 \\ 0.2x-1+0.05x=2.75 \\ 0.25x-1=2.75 \\ 0.25x=2.75+1 \\ 0.25x=3.75 \\ x=15 \end{gathered}$$

Therefore,

$$\begin{gathered} 2x-10=2\times 15-10 \\ =30-10 \\ =20 \end{gathered}$$