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?

Question

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?

in progress 0
Adeline 1 week 2021-09-15T01:18:48+00:00 1 Answer 0

Answers ( )

    0
    2021-09-15T01:20:31+00:00

    Answer:

    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.  

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )