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?

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.