SOLUTION: Fran has 51 dimes and nickels. If the value of the coins is $4.10, how many more dimes than nickels are there?

Question 948389: Fran has 51 dimes and nickels. If the value of the coins is $4.10, how many more dimes than nickels are there?
Answer by jpvn2015(54) (Show Source): You can put this solution on YOUR website!
To solve this problem, we have to find out how many dimes and nickels constitute the value of $4.10. I believe the simplest way of doing this is by creating two separate equations. In this problem:
x = amount of nickels
y = amount of dimes
Thus, the two equations will be:
x + y = 51
0.05x + 0.10y = 4.10
Let's solve for x. To do this, multiple the bottom equation by 20, so that the x on the top equation will cancel out with the x on the bottom equation after subtraction:
x + y = 51
x + 2y = 82
Reverse the equation for logical standards:
x + 2y = 82
x + y = 51
Now, subtract the bottom from the top (the x's cancel out):
y = 31
Thus, there are 31 dimes. Since there are 51 total coins, there will be 20 (51-31) nickels.
31-20 = 11
Therefore, there are 11 more dimes than nickels.
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