Need an equation for a word problem...

Question

Suppose you go and buy 100 lbs of cucumbers that are 99% water. Unfortunately, you do not observe the rules of caring for your cucumbers so after some time they dehydrate until they are only 98% water. How much do they then weigh?

Answer 1

The water content is proportional to the weight of the cucumbers.  This means the less water content, the less the cucumbers weigh.  The cucumbers did not loss too much water content, so the new weight should be a little under 100 lbs.

 

Set up the proportion.

 

Ratio of weight = ratio of water content in percent

 

100 / x = 99 / 98

 

where x represents the weight after the water loss.

 

Solve for x.

Answer 2

w represents the final weight

 

100 : 99 :: w : 98          product of means/extremes

9800 = 99w                  divide both sides by 99

98.98 = w

 

Have looked at Arthur D.'s response.

Still thinking.

Answer 3

 

100 lbs of cucumbers that are 99% water

this means that 99 lbs are water and only 1 lb is actually the vegetable

they dehydrate until they are only 98% water

this means that 2% of the weight is the vegetable

the amount of vegetable does not change

we determined that 1 lb is actually vegetable, which again is now 2% of the weight

setting up an equation...

1 is 2% of what number ?

1=2%*n

1=0.02*n

n=1/0.02

n=100/2

n=50 lbs

the cucumbers now weigh only 50 lbs (answer)

check: 1 lb is vegetable so 49 lbs is water, 49/50=98/100=98% water

now that you see the answer here is a simpler solution...

98%=98/100 is water and 2%=2/100 is vegetable

98/100=49/50 is water and 2/100=1/50 is vegetable

49 lbs water and 1 lb vegetable makes 49+1=50 lbs