SOLUTION: Suphie has some coins. She has 3 more quarters than nickels and 2 more times than quarters. if the she has 7 nickels, how much money does she have?

Question 656991: Suphie has some coins. She has 3 more quarters than nickels and 2 more times than quarters. if the she has 7 nickels, how much money does she have?
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
First off, I guess this should say "2 more dimes than quarters." That would make more sense.
Let n,d,q be the number of nickels, dimes, and quarters respectively.
Statement 1: 3 more quarters than nickels
q = n + 3
Statement 2: 2 more dimes than quarters
d = q + 2
Statement 3: 7 nickels
n = 7
Putting this all together:
Using statement 3, we get that q = 7 +3 = 10. So q = 10
Then using statement 2, we get that d = 10 +2 = 12
So, we have 7 nickels, 12 dimes, 10 quarters.
Thus we have (.05)*7 + (.10)*12 + (.25)*10 = .35 + 1.20 + 2.50 = $4.05
Suphie has $4.05.
There's no need to be this elaborate when doing these problems, but it never hurts to outline everything ad nauseum (to the point of nausea), until you get the basics down. Then you'll start to realize, okay she has 7 nickels, well she has 3 more quarters so that's 10, and 2 more than quarters to make dimes is 12. It takes practicing writing out these equations first before you get to that point.

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