# Solving a linear equation from a mixture word problem

Ok so I already know how to throw a word problem into a mixture solution table. In this situation I am going to go ahead and throw the equation at you guys and see if you can help me figure out this equation.

$$.1x + .4(100 - x) = 31$$

So this is what I would do:

$$(.1x / 100 ) + (.4 / 100)(100 - x) = 31$$

which turns into:

$$(100)(.1x / 100 ) + (.4 / 100)(100 - x) = 31(100)$$

which turns into:

$$1 + 4(100 - x) = 3100$$

and so on...

I recently found out I was not supposed to divide the $.1x$ and $.4$ by $100$, but divide by $10$ instead of $100$.

This baffles me, why would I divide the decimals by $10$ instead of $100$?

• Your last equation is missing something: the $\ x \$ that was present in the first term all along the way has suddenly disappeared. You should have $\ x \ + \ 4 \ (100 - x ) \ = \ 310 \ ,$ as otherwise corrected by nagniemerg. – colormegone Jan 22 '14 at 5:24

## 1 Answer

When you multiply .1 by 100, you do not get 1. That is .1 = 1/10 and not 1/100.

So then your equation becomes

10 + 40(100-x) = 3100.

You could have just multiplied by 10 instead and gotten

1 + 4(100-x) = 310.

Solve for x.

• And now my mind has been blown. Thank you so much, I feel so dumb now haha. It is just simple math, here I am just trying to follow step 1, 2, and 3 instead of actually trying out to see what happens when you multiply 100 by .1. blah – User 101 Jan 22 '14 at 4:53