Question 260394: Word problem: A storekeeper goes to the bank to get $10 worth of change. She requests twice as many quarters as half dollars, twice as many dimes as quarters, three times as many nickels as dimes, and no pennies or dollars. How many of each coin did the storekeeper get?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! no. of each coin represented by: n, d, q, h
:
Write an equation for each statement
:
A storekeeper goes to the bank to get $10 worth of change.
.05n + .10d + .25q + .50h = 10.00
:
We are going to get everything in terms of d.
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She requests twice as many quarters as half dollars,
q = 2h
:
twice as many dimes as quarters,
d = 2q
or
q = .5d
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three times as many nickels as dimes,
n = 3d
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In the equation q = 2h, replace q with .5d from the equation q =.5d
.5d = 2h
d = 4h
or
h = .25d
:
.05n + .10d + .25q + .50h = 10.00
Substitute
.05(3d) + .10d + .25(.5d) + .50(.25d) = 10.00
:
.15d + .10d + .125d + .125d = 10.00
.5d = 10
d = 10/.5
d = 20 dimes
and
q = .5d
q = .5(20)
q = 10 quarters
and
n = 3d
n = 3(20)
n = 60 nickels
and
h = .25d
h = .25(20)
h = 5 halfs
:
See if that works
.05(60) + .10(20) + .25(10) + .5(5) =
3.00 + 2.00 + 2.50 + 2.50 = 10.00
:
Summarize: 60 nickels, 20 dimes, 10 quarters, 5 half$
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