Answer:
The number of nickels is 47
Step-by-step explanation:
1 nickel is 5 cents while 1 quarter is 25 cents
let the number of nickels be n and the number of quarters be q
From the question;
the number of nickels n is 8 more than half the number of quarters (q/2)
n = q/2 + 8
(n-8) = q/2
q = 2(n-8) = 2n - 16 ••••(i)
let us convert $21.85 to cents
there are 100 cents in $1
Thus; $21.85 will be 21.85 * 100 = 2185 cents
1 nickel is 5 cents; so n nickels will be 5 * n = 5n cents
1 quarter is 25 cents; so q quarters will be 25 * q = 25q cents
The addition of both will give 2185 cents
Thus;
5n + 25q = 2185 ••••••(ii)
Substitute equation i into ii
5n + 25(2n-16) = 2185
5n + 50n - 400 = 2185
55n = 2185 + 400
55n = 2,585
n = 2,585/55
n = 47 nickels
