Answer:
25 nickels and 23 quarters
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.