Question 59411
A clerk was asked to change a $10 bill.  She returned 9 more dimes than nickels and 21 more quarters than dimes.  How many of coins of each did she return?
:
We can avoid decimals if we do this in terms of cents instead of dollars:
:
Let the amount of nickels be: x
Then the amount of money in nickles is: 5x  in cents
:
The amount of dime is 9 more than nickles: x+9
Then the amount of money in dimes is: 10(x+9) in cents
:
The amount of quarters is 21 more than dimes: (x+9)+21=x+30
Then the amount of money in quarters is: 25(x+30)  in cents
:
She has a total of: $10.00 or 1000 in cents
So add all the amounts to = 1000
Problem to solve:
5x+10(x+9)+25(x+30)=1000
5x+10x+90+25x+750=1000
40x+840=1000
40x+840-840=1000-840
40x=160
40x/40=160/40
x=4
The amount of nickels: x=4
The amount of dimes: x+9=4+9=13
The amount of quarters: x+30=4+30=34
:
To check add 4 nickels, 13 dimes and 34 quarters and see if you get $10.
$.05(4)+$.10(13)+$.25(34)=$10.00 ?
$.20+$1.30+$8.50=$10.00  ?
$10.00=$10.00 !!! Yeah!!!
Happy Calculating!!!