How Much Water Evaporated?Date: 06/19/2003 at 14:36:44 From: Amanda Subject: Mixtures and percents A substance is 99% water. Some water evaporates, leaving a substance that is 98% water. How much of the water evaporated? We know that 50.5% of the water evaporates, but have no idea how to create a generalized equation for this problem. Date: 06/20/2003 at 00:24:46 From: Doctor Ian Subject: Re: Mixtures and percents Hi Amanda, Let's say we start with W units of water, and S units of other stuff. We originally have 99% water, so W 99 --- = --- W+S 100 Now we want to reduce the water to some fraction, F, of the original amount. And we want to end up with 98% water: FW 98 ---- = --- FW+S 100 We can solve each of these equations for S: W 99 --- = --- W+S 100 100W = 99(W+S) 100W = 99W + 99S W = 99S W/99 = S and FW 98 ---- = --- FW+S 100 100FW = 98(FW+S) 100FW = 98FW + 98S 2FW = 98S 2FW/98 = S Two things equal to the same thing are equal to each other, so W/99 = 2FW/98 1/99 = 2F/98 98/(99*2) = F 0.495 = F So 49.5% of the water remains, which means that 50.5% evaporated. Here's a similar problem. Suppose there are 198 men and 2 women in a room. That is, the men make up 99% of the people in the room. How many men have to leave for the percentage of men to drop to 98%? It's easier to see the answer if you concentrate on the women instead of the men. The women originally make up 1% of the people in the room. Later, they make up 2%. For 2 women to make up 2% of a room, there have to be 100 people in the room. So there have to be 98 men. Which means 100 of the men had to leave. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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