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

Question

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

anonymous · Answer

$$.25x+.05(178-x)=31.50$$

anonymous · Answer

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 · Answer

I always end up forgetting a variable or something.

anonymous · Answer

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

anonymous · Answer

it looked good to me!

hero · Answer

Satellite, how do you avoid making typing mistakes?

hero · Answer

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 · Answer

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.