Question 603226: Greg has 6.25 in quarters,dimes,and nickels. If he has twice as many quarters as dimes and twice as many dimes as nickels,how many of each coin does he have?? Please help it's very confusing i have tried but went over the amount($6.25)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Greg has 6.25 in quarters,dimes,and nickels.
If he has twice as many quarters as dimes and twice as many dimes as nickels, how many of each coin does he have?
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Let q = no. of quarters
Let d = no. of dimes
Let n = no. of nickels
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Write an equation for each statement:
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"Greg has 6.25 in quarters,dimes,and nickels. "
.05n + .10d + .25q = 6.25
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"If he has twice as many quarters as dimes"
q = 2d
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"and twice as many dimes as nickels,"
d = 2n
or we can divide both sides by 2 and have
n = .5d
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Now we have everything in terms of d
.05n + .10d + .25q = 6.25
replace q with 2d, replace n with .5d
.05(.5d) + .10d + .25(2d) = 6.25
.025d + .10d + .50d = 6.25
.625d = 6.25
d = 
d = 10 dimes
then
q = 2d
q = 2(10)
q = 20 quarters
and
n = .5d
n = .5(10)
n = 5 nickels
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See if that works out
.05(5) + .10(10) + .25(20) =
.25 + 1.00 + 5.00 = 6.25, confirms our solution of 5 nickles, 10 dimes, 20 quarters
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Did this unconfuse you somewhat?
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