> solve the following problem. it may be to draw a chart on scrap paper to organize the information and write the equation. be sure to show all steps (v. e.s. t.) and work in order to receive full credit.

a clerk was asked to change a $10 bill. she returned 9 more dimes than nickels and twenty-one more quarters than dimes. how many coins of each did she return?

The answer is 4 nickles, 13 dimes, and 34 quarters.

d - number of dimes
n - number of nickels
q - number of quarters

The value of 1 nickel is $0.05.
The value of 1 dime is $0.10.
The value of 1 quarter is $0.25.

A clerk was asked to change a $10 bill:
0.05n + 0.10d + 0.25q = 10
She returned 9 more dimes than nickels:
d = n + 9
She returned twenty-one more quarters than dimes:
q = d + 21 = n + 9 + 21 = n + 30

We have:
0.05n + 0.10d + 0.25q = 10
d = n + 9
q = n + 30

Substitute d and q into the first equation:
0.05n + 0.10(n + 9) + 0.25(n + 30) = 10
0.05n + 0.10n + 0.90 + 0.25n + 7.5 = 10
0.05n + 0.10n + 0.25n + 0.90 + 7.5 = 10
0.40n + 8.40 = 10
0.40n = 10 - 8.40
0.40n = 1.60
n = 1.60 : 0.40
n = 4


d = n + 9
n = 4
d = 4 + 9 = 13


q = n + 30
n = 4
q = 4 + 30 = 34