## 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?

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

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.

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.