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30 May, 12:16

Dillon has saved 57 coins in his piggy bank. The coins are a mixture of quarters and dimes. He has saved $12 so far. Let q = # of quarters and d = # of dimes.

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Answers (2)
  1. 30 May, 14:53
    0
    Dillion has 42 quarters and 15 dimes.

    Step-by-step explanation:

    Let the number of quarters=q

    Let the number of dimes=d

    Dillon has saved 57 coins in his piggy bank.

    Therefore:

    q+d=57

    Now, 1 dime=$0.10 and 1 quarter=$0.25.

    We multiply the value of each coin by the number of coins present.

    Since Dillion has a total of $12

    Therefore:

    0.1d+0.25q=12

    We solve the two equations simultaneously.

    From equation 1, q=57-d

    Substitute q=57-d into 0.1d+0.25q=12

    0.1d+0.25 (57-d) = 12

    0.1d+14.25-0.25d=12

    0.1d-0.25d=12-14.25

    -0.15d=-2.25

    Divide both seides by - 0.15

    d=15

    Recall: q=57-d

    q=57-15=42

    Therefore, Dillion has 42 quarters and 15 dimes.
  2. 30 May, 16:15
    0
    Answer: 42 quarters and 15 dimes.

    Step-by-step explanation:

    If q is the number of quarters, and d the number of dimes, we have that:

    q + d = 57

    q*0.25 + d*0.10 = 12

    the first step is isolating one of the variables in one of the equation, it is easier to do it in the first one, let's isolate q.

    q = 57 - d

    now, we can replace this in the second equation and solve it for d.

    q*0.25 + d*0.10 = 12

    (57 - d) * 0.25 + d*0.10 = 12

    57*0.25 + d * (0.10 - 0.25) = 12

    57*0.25 - d*0.15 = 12

    -d*0.15 = 12 - 57*0.25 = - 2.25

    d = (-2.25) / (-0.15) = 15

    So the number of dimes is 15, this means that the number of quarters must be:

    q = 57 - d = 57 - 15 = 42
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