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24 September, 13:24

The numbers if nickels and quarters in a bank are in the ratio 23:25. If the coins are worth $7, how mnay of each type are there?

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  1. 24 September, 13:32
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    25 nickels and 23 quarters

    Step-by-step explanation:

    The smallest possible integer solution is 23 nickels and 25 quarters.

    23*0.05 + 25*0.25 = 1.15 + 6.25 = $7.40.

    That's already over $7.00.

    We can't solve the problem as stated unless we use fractional numbers of coins, and that's impossible.

    Assume the correct ratio is 25/23

    Let n = number of nickels

    and q = number of quarters. Then we have two conditions.

    (1) n/q = 25/23

    (2) 0.05n + 0.25q = 7

    (3) n = (25/23) q Multiplied (1) by q

    (4) 0.05 (25/23) q + 0.25q = 7 Substituted (3) into (1)

    0.05435q + 0.25q = 7 Simplified

    0.3043q = 7 Combined like terms

    (5) q = 23 Divided each side by 0.3043

    n/23 = 25/23 Substituted (5) into (1)

    n = 25 Divided each side by 23

    There are 25 nickels and 23 quarters.

    Check:

    (1) 25/23 = 25/23 (2) 0.05*25 + 0.25*23 = 7

    1.25 + 5.75 = 7

    7 = 7

    OK.
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