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

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) (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 . Multiply EVERY term by 100 (to make every number whole) to get

So the first equation is

Also, "the number of dimes was doubled and the number of nickels was decreased by 10, the value would be $9.85" means that . Distribute to get . Multiply EVERY term by 100 to make every number positive. So we now get . Add 50 to both sides to get

So the second equation is

So we have the system of equations:

Multiply the both sides of the first equation by -1.

Distribute and multiply.

So we have the new system of equations:

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

Group like terms.

Combine like terms.

Simplify.

Divide both sides by to isolate .

Reduce.

------------------------------------------------------------------

Now go back to the first equation.

Plug in .

Multiply.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So our answers are and .

This means that there are 35 nickels and 43 dimes
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