You have 100 pounds of potatoes, which are 99 percent water by weight. They dehydrate until they’re 98 percent water. How much do they weigh...

Let:

d = Weight of completely
dehydrated potatoes

n = Percentage of water in
potatoes

p(n) = Weight of potatoes having n percent
water.

Then for a given value of n and p(n) the value of d
is given by formula:

d = p(n)*(100 -
n)/100

And for a given value of d and n weight of potatoes
is given by the formula:

Weight of potatoes = 100*d/(100 -
n)

Substituting, in above equation, given value of p(n) and
n for potatoes with 99 percent water:

d = 100*(100 -
99)/100 = 1 pound

Substituting this value of d and
percentage of water as 98, in the equation for weight of potatoes we
get:

Weight of potatoes wit 98 percent water = 100*1*/(100
- 98)

= 50 pounds

Please note
that in this 50 pounds of potatoes with 98 percent water, the weight of dried potato
remains 1 pound, and the weight of water becomes 49 pounds. This amounts to 2 percent
dried potatoes and 98 percent water.