Super hard percentage thing!!!!!!!!! TOOO HARD

[jebby]

OMG This question has been bugging me for DAYS. SO HARD. This is the question:

THE POTATO PARADOX!!!
You buy 100 kg of potatoes which are 99% water by weight . You spread them out on your back porch in the sun to dry out. As they begin to dry water begins to evaporate. After a while enough water has evaporated so that the potatoes are now 98% water. If you were to weigh the potatoes at this point, what would they weigh?

IF ANYONE CAN GET THIS, I'LL BE SURPRISED.:cool::cool::cool::cool::cool::cool::cool::cool:
But I don't think so.
Good Luck
Jebby McFebby

 

[soroban]

Hello, jebby!

This is basically a "mixture problem".
Do you have a procedure for that?

You buy 100 kg of potatoes which are 99% water by weight.
You spread them out on your back porch in the sun to dry out.
After a while, enough water has evaporated so that the potatoes are now 98% water.
If you were to weigh the potatoes at this point, what would they weigh?

We have 100 kg of potatoes which contain 99% water.
. . It has: .\(\displaystyle 99\%\times 100 \,=\,99\text{ kg water.}\)


Let \(\displaystyle x\) = kg of water evaporated.
. . That is, \(\displaystyle x\) kg of water is removed.

Hence, the final result has: .\(\displaystyle 99 - x\text{ kg of water.}\) .*


But the final result is \(\displaystyle 100-x\) kg of potatoes which contain 98% water.
. . That is, it has: .\(\displaystyle 0.98(100-x)\text{ kg water.}\) .*


We just described the final amount of water in two ways.

There is our equation! . . . . . \(\displaystyle 0.98(100-x) \:=\:99 - x\)


Solve for \(\displaystyle x\!:\;\;98 - 0.98x \:=\:99-x \quad\Rightarrow\quad0.02x \:=\:1 \)

. . . . . \(\displaystyle x \:=\:\frac{1}{0.02} \quad\Rightarrow\quad x \:=\:50\)


Hence, 50 kg of water is removed.

. . The final result weighs 50 kg.