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?
My Set Up:
n + d = 6.05..............Equation A
(n - 10) + 2d = 9.85...Equation B
I realize that we have two equations in two unknowns.
What is wrong with my equations?
I keep getting a negative answer for coins and this does not make sense.
If you're talking in "amounts", you need to multiply the number of dimes and nickels by their respective values.
Let n = the number of nickels
Let d = the number of dimes
Your first equation becomes:
 5n + 10d = 605
Now, let's work on the changes.
Let n-10 = the new number of nickels
Let 2d = the new number of dimes
Your second equation becomes:
 5(n - 10) + 10(2d) = 985
You can simplify both equations to the following:
 n + 2d = 121
 n + 4d = 207
Subtract the two equations to get:
-2d = -86
d = 43
So the number of dimes = 43 to make $4.30
The number of nickels can be found by subtracting $4.30 from $6.05 to get $1.75 and dividing by $.05, we get 35 nickels
Let's check it:
43 dimes = $4.30
35 nickels = $1.75
Total = $6.05
Now, let's double the dimes, and reduce the number of nickels by 10.
86 dimes = $8.60
25 nickels = $1.25
Total = $9.85