Answer:
Jack has 8 Dimes.
Explanation:
Dime = $0.1
Nickel = $0.05
D = The number of Dimes Jack has.
N = The number of Nickels Jack has.
Jack has $1.55 in nickles and dimes.
0.1D + 0.05N = 1.55
He has 7 more nickles than dimes.
D + 7 = N
I will convert the first equation to integers by multiplying by 20 so 1 coefficient is the same in both equations.
2D + N = 31
Rearrange the second equation.
D + 7 = N becomes N - D = 7
Subtract the equations to remove a coefficient.
(2D + N) - (N - D) = 31 - 7
(2D - - D) + (N - N) = 31 - 7
3D = 24
D = 8
Jack has 8 Dimes. Therefore, Jack has 15 Nickels.
We can check this is correct by substituting 8 into the original equations.
Jack has $1.55 in nickles and dimes.
0.1(8) + 0.05N = 1.55
0.8 + 0.5N = 1.55
0.5N = 1.55 - 0.8
0.5N = 0.75
N = 0.75/5
N = 15
He has 7 more nickles than dimes.
(8) + 7 = N; N = 15