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- anonymous

A jar contains $31.50 in nickels and quarters. There are 178 coins in the jar. How many quarters are in the jar?

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- anonymous

\[.25x+.05(178-x)=31.50\]

- anonymous

put x = number of quarters, which have a total value of .25x, and since there are 178 coins total if there are x quarters there are 178 - x nickels which have a total value of .05(178-x)

- Hero

I always end up forgetting a variable or something.

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- anonymous

add them up and get there combined value
\[.25x+.05(178-x)=31.50\]

- anonymous

it looked good to me!

- Hero

Satellite, how do you avoid making typing mistakes?

- Hero

What I meant to write was:
n + q = 178
.05n + .25q = 31.50
The first time I forgot the q in the second equation. That's why I deleted it.

- mathmate

178 coins in quarters (0.25$) and nickels (0.05$) are worth $31.50.
If you don't have a calculator, nor pen and paper, this is how you would do it:
178 quarters are worth $44.50, that's $13 too much.
In changing a quarter for a nickel, we reduce by 0.25-0.05=$0.20. So we would change $13/0.02=65 quarters for nickels.
So we have 65 nickels and 178-65=113 quarters.

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