SOLUTION: A storekeeper goes to the bank to get $10 worth of change. She request twice as many quarters as half dollars, twice as many dimes as quarters, three times as many nickels as dimes

Question 296337: A storekeeper goes to the bank to get $10 worth of change. She request 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 store keeper get?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A storekeeper goes to the bank to get $10 worth of change.
She request 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 store keeper get?
:
"get $10 worth of change."
.05n + .10d + .25q + .50h = 10.00
:
"twice as many quarters as half dollars,"
q = 2h
h = .5q
replace .5 q with d (see next equation)
h = d
:
" twice as many dimes as quarters,
d = 2q
.5q = d
Multiply both sides by 2
q = 2d
:
" three times as many nickels as dimes,"
n = 3d
:
.05n + .10d + .25q + .50h = 10.00
:
Write total$ equation in terms of d
.05(3d) + .10d + .25(2d) + .5(d) = 10
:
.15d + .10d + .50d + .5d = 10
:
1.25d = 10
d =
d = 8 dimes
then
n = 3(8) = 24 nickels
and
q = 2(8) = 16 quarters
and
h = 8 half dollars
:
:
See if that adds up
.05(24) + .10(8) + .25(16) + .50(8) =
1.20 + .80 + 4.00 + 4.00 = $10; confirms our solutions

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