Dried Apricots

The Fall 2018 semester is less than 2 weeks away, and so what better time to talk to you about drying some Apricots. This is a very basic problem that I hope many of you can solve on your own. For those of you that cannot, I believe you will be able to understand the solution without too much difficulty.

The 133rd Riddle put out by The Riddler included the following Eternal question about percentages:

You loaded a drying shed containing 1,000 kilograms of apricots. They were 99 percent water. After a day in the shed, they are now 98 percent water. How much do the apricots weigh now?

First of all, you should try this problem on your own.  I think you can get it.  Before you do, however, at least get a guess.  That is the point of the problem, since even I was a little surprised by the answer.

The Solution

I’ll talk you through it first, so that you can perhaps follow how a mathematician would do it afterwards.

If 99% of 1000 kilograms is water, than 990 kilograms of the apricots is water, leaving 10 kilograms (1%) of what will eventually be the purely dried-out apricots. These are all the initial values prior to the apricots going in the shed.

Now, they are left in the shed for a day, and some of the water has evaporated out of the apricots. We need to understand that the total weight of the apricots and the weight of the water has both decreased by some amount (the water that evaporated).  We also need to understand that the 10 kilograms of dried apricots to-be has not changed.

If we are given that the apricots are now 98% water we want to deduce that the 10 kilograms of dried apricots to-be now represents 2% of the entire weight, rather than the original 1%.

So, 2% of what is equal to 10?  That can be quickly found by dividing 10 by .02, which gives you 500. The answer is 500 kg.

Wait, what? The weight decreased by half?  Did I do this right?

Indeed, we have, as you can check the answer seeing that both 500-10=490 and 0.98*500 = 490.

A mathematician would have given the unknown and desired quantity of the weight of apricots after a day some variable name, like w. Then, she would have set up the equation .02w=10, and solved for w by dividing both sides by .02.

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