SOLUTION: The cash register�s till only has 102 coins, made up of dimes and nickels. It contains $5.85 less in nickels than in dimes. How many dimes and nickels are there?

Question 1106585: The cash register�s till only has 102 coins, made up of dimes and nickels. It contains $5.85 less in nickels than in dimes. How many dimes and nickels are there?
Answer by greenestamps(13330) (Show Source): You can put this solution on YOUR website!

There are many different ways to set up this problem for solving. It would be good for you to know several different ways, since in similar problems it might be clear that one method is better than the others.

So I will suggest several different ways to get started; then you can do the actual solving on your own.

(1) Using two variables, n for nickels and d for dimes:
[the total number of coins is 102]
[the value of the n nickels, at 5 cents each, is $5.85 (585 cents) less than the value of the d dimes, at 10 cents each.]
Solve the pair of equations by any method you like.

(2) Using only variable n for the number of nickels; since the total number of coins is 102, the number of dimes will be (102-n).
[this is the same equation as the second equation above, using only one variable, n]

(3) Using only variable d for the number of dimes; since the total number of coins is 102, the number of nickels is (102-d).
[this is again the same equation..., using variable d]

With the second and third methods of setting up the problem, you have to solve only one equation in a single variable, while in the first method you have to solve a pair of equations. For this reason, I personally much prefer using a single variable. However, many people prefer using two variables, probably because it is easier to understand how to set up the initial equations.
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