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6 April, 06:12

You have have a jar containing 72 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $8.40. How many of each type of coin do you have?

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  1. 6 April, 06:45
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    Total number of coins: T=72

    Number of quartes ($0.25) : q=?

    Number of nickels ($0.10) : n=?

    Number of quarters + Number of nickels = Total number of coins

    q+n=72 (Equation 1)

    Total Value of the coins in the jar: V=$8.40

    Value of the quarter's coins: $0.25q

    Value of the nickel's coins: $0.05n

    Value of the quarter's coins + Value of the nickel's coin=Total value of the coins in the jar

    $0.25q+0.05n=$8.40

    0.25q+0.05n=8.40 (Equation 2)

    We have a system of 2 equations and 2 unknowns (q and n):

    (1) q+n=72

    (2) 0.25q+0.05n=8.40

    Using the method of substitution:

    Let's isolate q in the first equation:

    (1) q+n=72

    (1) q+n-n=72-n

    (1) q=72-n

    Let's replace q by 72-n in the second equation:

    (2) 0.25q+0.05n=8.40

    0.25 (72-n) + 0.05n=8.40

    Applying the distributive property:

    (0.25) (72) - 0.25n+0.05n=8.40

    Multiplying the constant terms and adding similar terms of the variable n:

    18-0.20n=8.40

    Isolating n:

    18-0.20n-18=8.40-18

    -0.20n=-9.6

    (-0.20n) / (-0.20) = (-9.6) / (-0.20)

    n=48

    Replacing n by 48 in the first equation:

    (1) q=72-n

    q=72-48

    q=24

    We have 24 coins of quarters and 48 coins of nickels
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