Martian Potato Paradox Solution

Matt Damon has 100 pounds of Martian potatoes, which are 99% water by weight. For complex scientific purposes, he needs to dehydrate them until they are 98% water. After he completes this task, how much do the Martian potatoes weigh now?

How’d it go? We’re you able to solve the paradox? Did you use the hint and help from the last lesson?

I have two possible solutions for you. The first solution requires only basic math with the option of using pre-algebra. The second solution uses algebra. Pick whichever suits your fancy!

Basic Math Solution

The potatoes are 99% water, so begin by finding 99% of 100 pounds to determine the weight of water beforehand.

99% of 100 is 99, so the potatoes are 99 pounds water and 1 pound potato matter.

We need to determine how much the potatoes will weigh after dehydrating them to 98 percent water. The potato matter won’t change when we dehydrate them, so keep the potato matter equal to 1 pound.

If the potatoes are 98% water, then 2% is potato matter. Therefore 2% of the total weight must equal 1 pound of potato matter.

Our question is then: 2% of what equals 1 pound?

(Note: if you know pre-algebra, you can skip to the alternative ending)

Let’s think about this visually.

Suppose I had 10 pounds of potatoes composed of 1 pound potato matter and 9 pounds water.

The shaded portion is 10% of the bar. This can be calculated by multiplying 1/10 by 10/10 to yield 10 per 100 = 10 percent.

10% is too large. Remember we are looking for a portion makes 1 pound equal to 2% of the total weight.

Let’s make the diagram 5 times larger. Fill in 1 square to represent 1 pound of potato matter.

To find out how much this would be per one hundred, multiply 1/50 by 2/2.

2/100 is equivalent to 2 percent!

After dehydrating, we will have 50 pounds of potatoes that are 1 pound potato matter and 49 pounds water.

This equates to 2% potato matter and 98% water as expected. Therefore, we need to dehydrate the potatoes by 50 pounds in order to obtain 98 percent water!

And that’s why it’s called a paradox. It seems like in order to reduce the weight by 1 percent we wouldn’t have to dehydrate them much at all. But in fact we have to reduce the weight by half of the original!

Alternative Ending using Pre-algebra

Using pre-algebra you can take a shorter path. Remember when we deduced that what we were really trying to solve was: 2% of what is 1 pound?

Translate the statement into an equation using the following keywords:

  • 2% => 2/100
  • of => •
  • what => x

We then obtain:

Multiply both sides by 100 to undo the division by 100.

Divide both sides by 2 to undo the multiplication by 2.

After dehydration we have 50 pounds of potatoes left which are 1 pound potato matter and 49 pounds water.

The Algebraic Solution

For those of you who like variables and equations, this is the solution for you! We need to calculate the amount of water lost during dehydration.

We’ll begin with a simple objective:

The water weight before is 99% of 100 pounds. The water weight after will be 98% of the total weight. The total weight will be 100 pounds minus the amount lost from dehydration, call this unknown amount x.

To solve the equation, begin by distributing the .99 and .98 through.

Note negative .98 times negative x results in positive .98x

Subtract 98 from 99.

Subtract .98x from both sides.

Rewrite x as 1x

Divide both sides by 0.02.

Therefore the weight in water to be removed is 50 pounds. Since the original weight was 100 pounds, the remaining weight after dehydration will be 50 pounds as well. Because 1 pound is potato matter, there will be 49 pounds of water in the dehydrated potatoes.

You can check the answer by dividing 49 by 50 to ensure the potatoes are 98% water.

Multiply the decimal value by 100 to yield the percentage.

Strange isn’t it? Reducing the water by 1 percent requires us to cut the total weight of the potatoes in half! That’s the paradox.

Next Lesson: Understanding Logarithms and Roots

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