# Math

You have some quarters and some nickels in your pocket in total you have 7 coins and together they are worth 95 cents how many nickels and how many are quarters?

I know the equations will have something to do with the 7 couns and they are worth 95 cents all together

Is one of them x+y=95

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1. I know that there will be 3 quarters and 4 nickels because 3 quarters is 75cents and 4 more nickels equals 95, but how would I make 2 equations for the problem.

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posted by M
2. Actually one of them is x+y=7

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posted by M
3. right. x+y=7
that counts the coins. Now you have to count the value.

If you have x nickels and y quarters, then

5x+25y = 95

Now, you can insert your first equation into this one as follows:

5x+5y+20y = 95
5(x+y)+20y = 95
5(7)+20y = 95
35+20y = 95
20y = 60
y=3
so, x=4

That is how to arrive at the solution algebraically, rather than just guessing.

There are also other ways to manipulate the equations, but this one seemed quite natural to me.

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posted by Steve

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