Question

Jaime has $$2.60$in dimes and nickels. The number of dimes is 14 more than the number of nickels. How many of each coin does he have?

Short answer

The number of nickels are$8$and dimes are$22$.

Step-by-step solution

Step 1. Assumption Of variables

Let he number of nickels be $x$

Therefore ,

According to the question,

number of dimes will be$14+x$

Value of each dime$=0.10$

The total value of dimes will be$0.10(x+14)$

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,

$$\begin{gathered} 0.10(x+14)+0.05x=2.60 \\ 0.10x+1.4+0.05x=2.60 \\ 0.15x+1.4=2.60 \\ 0.15x=2.60-1.4 \\ \frac{0.15x}{0.15}=\frac{1.2}{0.15} \\ x=8 \\ 14+x=14+8=22 \end{gathered}$$