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pre calc

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rose counted her money and found that her 25 coins which were nickels, dimes, and quarters were worth $3.20. The number of dimes exceeded the number of nickels by 4. How many coins of each kind did she have?

I know that the expression for nickles would be 5x, for dimes it would be
10x + 40, but i don't understand how to do the expression for quarters.....can someone help me with the answer

  • pre calc -

    N = number of nickles
    D = number of dimes = N+4
    Q = number of quarters
    = 25-N-D
    = 25-N-(N+4)
    = 21-(2N)

    Add the coins to get $3.20
    (N*$0.05) + (D*$0.10) + (Q*$0.25) = $3.20
    Expressing D and Q in terms of N:
    (N*$0.05) + ((N+4)*$0.10) + (21-2N)*$0.25=$3.20

    Solve for N. Then plug N into the equations for D and Q

  • pre calc -

    It is not clear what your x means, and where you came up with 10x + 40 for the value of the dimes. Let the numbers of nickels, dimes and quarters be N, D and Q.
    5 N + 10 D + 25 Q = 320
    D = N + 4
    N + D + Q = 25

    Now solve those three equations in three unknowns.

    5 N + 10(N + 4) + 25 Q = 320
    15 N + 25 Q = 280
    2 N + 4 + Q = 25
    Multiply that last equation by 25
    50 N + 25 Q = 525
    Now eliminate the Q
    35 N = 245
    N = 7
    You do the rest

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