SOLUTION: 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?

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?

Found 2 solutions by funmath, uma:
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
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!!!
Answer by uma(370) (Show Source): You can put this solution on YOUR website!
Let x be the number of nickels the clerk returned.
So number of dimes brought = x + 9
Number of quarters retuned = (x+9) + 21
= x + 30
Value of x nickels = 5x cents
Value of (x + 9) dimes = 10(x+9)
= 10x + 90 cents

Value of (x + 30) quarters = 25(x + 30)
= 25x + 750 cents
Total value = 1000cents
==> 5x + 10x + 90 + 25x + 750 = 1000
==> 40x + 840 = 1000
==> 40x = 160 [subtracting 840 from both the sides]
==> x = 4 [dividing by 40 on both the sides]
Number of nickels = 4
Number of dimes = 4 + 9 = 13
Number of quarters = 4 + 30 = 34
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