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Question 669400: Joe has a collection of nickels and dimes that is worth $5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45. How many dimes does he have?
This is the problem directly from my homework. I'm trying to figure out the system of equations so I can solve the problem. So far I've come up with
.1d+.05n=5.65 and 2(.1d)+.05n+8=10.45
but I keep ending up with d= -32 so I must be way off.
Found 2 solutions by ReadingBoosters, MathTherapy:
Answer by ReadingBoosters(3246)   (Show Source):
You can put this solution on YOUR website! .05n + .1d = 5.65
.05(n+8) + .1(2d) = 10.45
...
.05n + .1d = 5.65
.05n + .4 + .2d = 10.45
...
.05n + .1d = 5.65
.05n + .2d = 10.05
...
Multiply the first equation by -1 and add to the second
-.05n + .05n + -.1d + .2d = -5.65 + 10.05
.1d = 4.4
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Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Joe has a collection of nickels and dimes that is worth $5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45. How many dimes does he have?
This is the problem directly from my homework. I'm trying to figure out the system of equations so I can solve the problem. So far I've come up with
.1d+.05n=5.65 and 2(.1d)+.05n+8=10.45
but I keep ending up with d= -32 so I must be way off.
You are off, but not by that much. Looking at what I got and you got, I can see that your 2nd equation should have been .1(2D) + .05(N + 8) = 10.45. This is where your error is. The correct solution is below:
Let the original amount of dimes and nickels that he has be D, and N, respectively
Then: .1D + .05N = 5.65 ----- eq (i)
Doubling the amount of dimes would make the dimes, 2D
Increasing the nickels by 8 would make the amount of nickels, N + 8
Therefore, .1(2D) + .05(N + 8) = 10.45 ------ .2D + .05N + .4 = 10.45 ---- .2D + .05N = 10.05 ----- eq (ii)
.1D + .05N = 5.65 ---- eq (i)
.2D + .05N = 10.05 ---- eq (ii)
- .1D = - 4.40 --------- Subtracting eq (ii) from eq (i)
D, or original amount of dimes =  , or 
Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
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