Justin had nickels and dimes in his pocket. when he counted out his change he had $1.30. If he had 17 coins altogether, how many dimes did he have?

nickels --- x

dimes --- 17-x

solve:
5x + 10(17-x) = 130

To solve this problem, we can set up a system of equations.

Let's use the variables N and D to represent the number of nickels and dimes, respectively.

We are given two pieces of information:

1. The total value of his change is $1.30. Since each nickel is worth $0.05 and each dime is worth $0.10, we can write the equation:
0.05N + 0.10D = 1.30

2. The total number of coins is 17. So, we can also write the equation:
N + D = 17

Now, we can solve this system of equations to find the values of N and D.

First, let's solve the second equation for N:
N = 17 - D

Substitute this expression for N in the first equation:
0.05(17 - D) + 0.10D = 1.30

Simplify the equation:
0.85 - 0.05D + 0.10D = 1.30
0.05D = 1.30 - 0.85
0.05D = 0.45

Divide both sides of the equation by 0.05:
D = 0.45 / 0.05
D = 9

Therefore, Justin had 9 dimes in his pocket.