## Jack has \$1.55 in nickles and dimes. He has 7 more nickles than dimes. Find the number of dimes.

Question

Jack has \$1.55 in nickles and dimes. He has 7 more nickles than dimes. Find the number of dimes.

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1 week 2021-09-09T11:09:00+00:00 1 Answer 0

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