Question 12603: I know the result to this problem, but am having a hard time finding the equation that works for it. I spent 2 hours on it last night with no luck, can you help me please? The question is as follows:
Abby has 37 coins, consisting only of dimes and quarters, woth $7.45. How many dimes and how many quarters does she have?
I know that she has 25 quarters and 12 dimes, but that is form simple math.
Thanks for the help!!
Capesch
Answer by AdolphousC(70)   (Show Source):
You can put this solution on YOUR website! You need to set this up as a system of linear equations,
Define your varibles, Let D = # of Dimes, and Q = # of Quarters
First Equation is the one where you actually just count the coins...
D + Q = 37
Now, adding the value of the coins, here is where you count the money,
Dimes are worth 10 cents and quarters 25...
.1D + .25Q = 7.45
D + Q = 37
.1D + .25Q = 7.45
Now you have a simple system, I will multiply the top by .1
.1(D + Q = 37)
.1D + .25Q = 7.45
.1D + .1Q = 3.7
.1D + .25Q = 7.45 Now subtract the two equations
-.15Q = -3.75 Divide both sides by -.15
Q = 25
Now substitute into your original equations
D + Q = 37
D + 25 = 37 Subtract
D = 12
So she indeed has 25 Quarters and 12 Dimes
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