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## 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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## Answers ( )

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 = 23Divided each side by 0.3043n/23 = 25/23 Substituted (5) into (1)

n = 25Divided each side by 23There are

25 nickelsand23 quarters.Check:

(1)25/23 = 25/23(2)0.05×25 + 0.25×23 = 71.25 + 5.75 = 7

7 = 7

OK.