Question 787911: The question:
Brenda has $0.95 in nickels and dimes. There are 13 coins altogether. How many of each does she have?
What I have so far:
n + d = 13 coins
5n + 10d = 95
I was wondering what the next steps to solving this sort of equation were.
Found 2 solutions by solver91311, wilft1:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
There are several methods:
Substitution: Solve one of the equations for one of the variables in terms of the other. In your case, you might choose to solve your first equation for n in terms of an expression in d, as in  . Then substituting the expression part of this new equation for the solved for variable in the OTHER equation. Thus: \ +\ 10d\ =\ 95) . That gives you a single variable equation that you can solve by ordinary algebraic means.
Elimination: Multiply one (or both, if necessary) of your equations by a constant so that the coefficients on one of the varibles will be additive inverses in the two equations. For your example, multiply the first equation by -5 giving you  . Next, add the two equations term-by-term so that one of the variables is eliminated.  which simplifies to 
There are still other methods, Gauss-Jordan row reduction and Cramer's Rule, but we'll save all that for later, shall we?
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
Answer by wilft1(217)  (Show Source):
You can put this solution on YOUR website! your right as far as the equations go, easiest way to solve this is using the elimination method
n + d = 13
5n + 10d = 95
we need to eliminate one of our variables, so multiply the top line by -5
-5n - 5d = -65
5n + 10d = 95
we now add the two lines together, thereby eliminating 5n
5d = 30
divide both sides by 5
d = 6
we now know there are 6 dimes, plug that number back into the original equation to find out how many nickles there are...
5n + 10(6) = 95
5n + 60 = 95
5n = 35
n = 7
you have 7 nickles and 6 dimes
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