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.