SOLUTION: Emily has nickels, dimes, and quarters in her piggy bank. She has twice as many dimes as nickels and 12 fewer quarters than dimes. The total value of the coins is $9.00. How many o
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Question 278465: Emily has nickels, dimes, and quarters in her piggy bank. She has twice as many dimes as nickels and 12 fewer quarters than dimes. The total value of the coins is $9.00. How many of each coin type does Emily have?
This has had me confused for an hour. Can I get an explanation also? Thanks! Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Emily has nickels, dimes, and quarters in her piggy bank.
She has twice as many dimes as nickels and 12 fewer quarters than dimes.
The total value of the coins is $9.00.
How many of each coin type does Emily have?
:
Write an equation for each phrase
:
"She has twice as many dimes as nickels "
d = 2n
or divide both sides by 2 and you have:
n = .5d
:
"12 fewer quarters than dimes. "
q = (d - 12)
:
"The total value of the coins is $9.00."
.05n + .10d + .25q = 9.00
:
In the above equation, replace n with .5d, and replace q with (d-12)
.05(.5d) + .10d + .25(d-12) = 9.00
:
.025d + .10d + .25d - 3 = 9.00
:
.375d = 9 + 3
d =
d = 32 dimes
then
n = .5d
n = .5(32)
n = 16 nickels
and
q = d - 12
q = 32 - 12
q = 20 quarters
;
:
Check all this in the total$ equation
.05(16) + .10(32) + .25(20) =
.80 + 3.20 + 5.00 = 9.00
:
How about this? Did we eliminate some confusion about this?
The trick on these problems is to get all three unknowns in terms of one the
unknowns, d in this case.
