SOLUTION: 1. Joe has a collection of nickels and dimes that is worth $6.05. If the number of dimes was doubled and the number of nickels was decreased by 10, the value of the coins would be

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Question 199078: 1. Joe has a collection of nickels and dimes that is worth $6.05. If the number of dimes was doubled and the number of nickels was decreased by 10, the value of the coins would be $9.85. How many dimes does he have?
I have no idea where to start with this the best I can do is to subtract 6.05 from 9.85 but I don't know how to find the answer to this problem. I do have to show my work but I am confused.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let n=number of nickels and d=number of dimes

Since "Joe has a collection of nickels and dimes worth $6.05", this tells that 0.05n%2B0.10d=6.05. Multiply EVERY term by 100 (to make every number whole) to get 5n%2B10d=605

So the first equation is 5n%2B10d=605

Also, "the number of dimes was doubled and the number of nickels was decreased by 10, the value would be $9.85" means that 0.05%28n-10%29%2B0.10%282d%29=9.85. Distribute to get 0.05n-0.5%2B0.2d=9.85. Multiply EVERY term by 100 to make every number positive. So we now get 5n-50%2B20d=985. Add 50 to both sides to get 5n%2B20d=1035

So the second equation is 5n%2B20d=1035




So we have the system of equations:

system%285n%2B10d=605%2C5n%2B20d=1035%29


-1%285n%2B10d%29=-1%28605%29 Multiply the both sides of the first equation by -1.


-5n-10d=-605 Distribute and multiply.


So we have the new system of equations:
system%28-5n-10d=-605%2C5n%2B20d=1035%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28-5n-10d%29%2B%285n%2B20d%29=%28-605%29%2B%281035%29


%28-5n%2B5n%29%2B%28-10d%2B20d%29=-605%2B1035 Group like terms.


0n%2B10d=430 Combine like terms.


10d=430 Simplify.


d=%28430%29%2F%2810%29 Divide both sides by 10 to isolate d.


d=43 Reduce.


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-5n-10d=-605 Now go back to the first equation.


-5n-10%2843%29=-605 Plug in d=43.


-5n-430=-605 Multiply.


-5n=-605%2B430 Add 430 to both sides.


-5n=-175 Combine like terms on the right side.


n=%28-175%29%2F%28-5%29 Divide both sides by -5 to isolate n.


n=35 Reduce.


So our answers are n=35 and d=43.


This means that there are 35 nickels and 43 dimes