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

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    2021-09-09T11:10:40+00:00

    Answer:

    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

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