Jack has $1.55 in nickles and dimes. he has 7 more nickles than dimes. find the number of dimes.

Jack has 8 Dimes.

Step-by-step 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