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Evaporation

```Date: 12/08/2003 at 22:00:52
From: Olo
Subject: Mixture and percent

A substance is 99% water.  Some water eveporates, leaving a substance
that is 98% water.  How much of the water evaporated?
```

```
Date: 12/09/2003 at 01:52:54
From: Doctor Greenie
Subject: Re: Mixture and percent

Hi, Olo --

The original subtance is 99% water.  That means we have

# parts water
----------------------------------- = 99/100
total # parts of (water plus other)

So we can say we start with 99 parts water and 1 part other.

We take away x parts of water.  We then have (99-x) parts of water
and still 1 part other, giving us (100-x) parts of (water plus other).
The percentage of water in the new substance is 98%:

99-x
----- = .98
100-x

We solve this to determine x, the number of parts of water that
evaporate:

99-x = .98(100-x)

99-x = 98 - .98x

99-98 = -.98x + 1x

1 = .02x

50 = x

So 50 parts of water evaporated.  In terms of percentages, we started
with 99 parts water, and 50 of these parts evaporated, so the
percentage of water that evaporated is

50
-- * 100 = 50.5 (approximately)
99

You can find a different approach to the problem here:

How Much Water Evaporated?
http://mathforum.org/library/drmath/view/63108.html

I hope this helps.  Please write back if you have any further

- Doctor Greenie, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Ratio and Proportion
Middle School Word Problems

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