SOLUTION: Hi. I need help answering the following question. Thanks in advance. Sandy has $3.75 in change. She has three more quarters than dimes but twice as many nickels as quarters. Expre

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: Hi. I need help answering the following question. Thanks in advance. Sandy has $3.75 in change. She has three more quarters than dimes but twice as many nickels as quarters. Expre      Log On

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Question 151727: Hi. I need help answering the following question. Thanks in advance.
Sandy has $3.75 in change. She has three more quarters than dimes but twice as many nickels as quarters. Express as an algebraic equation and simplify.
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!

Let x = number of dimes
then
from:"She has three more quarters than dimes"
x+3 = number of quarters
from:"but twice as many nickels as quarters"
2(x+3) = number of nickels
.
Finally, since "Sandy has $3.75 in change" we derive our equation:
.10x + .25(x+3) + .05(2)(x+3) = 3.75
.10x + .25x + .75 + .10(x+3) = 3.75
.10x + .25x + .75 + .10x + .30 = 3.75
.45x + 1.05 = 3.75
.45x = 2.70
x = 6 (number of dimes)
.
x+3 = 6+3 = 9 (number of quarters)
.
2(x+3) = 2(6+3) = 2(9) = 18 (number of nickels)