lesson twenty

The Martian Potato Paradox

and a review of percents

Alright, have you’ve seen The Martian? If you haven’t, what are you doing reading about math? Seriously, stop what you’re doing and go watch it! Then come back and see me, pronto!

For the rest of you who have seen it, didn’t you love it?!

I did! But of course, I’m a real sucker for any movie that talks about math endearingly. After 2 hours and 21 minutes of science, math and engineering filled space drama, are you feeling inspired to tackle some math?

The Potato Paradox

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?

Hint

This problem can be solved with or without algebra. An algebraic equation may be helpful, but isn’t necessary at all. It can be solved with basic math alone.

Need Help?

If you are uneasy with percents, don’t worry I have a short review for you. Also see Lessons Eighteen and Nineteen for more help.

Review

A percent represents a portion per one hundred. For example, the following diagram represents 1% of 100 because 1 out of 100 dots is shaded.

This is equivalent to the fraction 1/100 or 0.01.

Therefore, the following are all equivalent:

Fractions are very similar to ratios. A ratio is a way of expressing the relationship between one thing and another, just like a fraction compares a part (the numerator) to the whole (the denominator).

Ratios can be expressed as fractions, in words, or using colons. For example, the ratio represented in the above picture can be written:

Note: Ratios are more flexible than fractions because we choose what we compare. In the example we compared the shaded dots to total dots, we could also have chosen to compare shaded to unshaded dots, which is a ratio of 2:3.

Suppose we want to find what 2/5 is equivalent to in decimal and percentage.

You could divide the fraction and multiply by 100 to find the percent.

Or you could use the ratio to determine how many there would be in 100 dots.

The ratio dictates that for every 5 dots, 2 are shaded. If I double the picture for 10 dots total, 4 dots will be shaded.

Percents represent parts per one hundred, so reproduce the picture ten times to yield 100 dots.

Maintaining the ratio, 40 dots are shaded which is 40 per 100 or 40 percent.

We can use the same thought process to manipulate fractions. Because 100 ÷ 5 = 20, multiply the fraction by 20/20 to yield a denominator of 100. This fraction indicates there are 40 shaded dots out of 100.

For the Potato Paradox, I recommend thinking about the problem in terms of a diagram and inspecting the ratios desired before and after. Good luck Earthlings!

Next Lesson: Martian Potato Paradox Solution

Thanks for reading!

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