ShmoopTube

00:04

Portions of Proportions, a la Shmoop.

00:07

Derek has recently noticed an interesting phenomenon. [Derek stood on a skating ramp]

00:10

There seems to be a direct proportion between the tricks he does on his skateboard…

00:13

…and the number of phone numbers he gets from girls. [Girl watching Derek skateboarding]

00:17

He’s sure he isn’t imagining it.

00:19

Just last week, he successfully completed a tough trick, and was awarded with three [Derek doing tricks on his skateboard]

00:22

phone numbers from cute, female bystanders.

00:25

Then yesterday, two tricks…six phone numbers.

00:28

This morning, he nailed THREE tricks, and got NINE phone numbers out of the deal. [Derek doing tricks on his skateboard and 9 girls phone numbers appear]

00:33

If this is, in fact, not mere coincidence…

00:35

…how many skateboard tricks has Derek performed if he’s been given 81 phone numbers?

00:41

First of all…we’d like to know where this skateboard park is that gets that kind of an audience. [Girls clapping Derek on a skateboard]

00:46

Unless it’s smack-dab in the middle of Madison Square Garden, we’re a little confused.

00:50

But okay. Suspension of disbelief.

00:52

What Derek has realized is that there is a mathematical proportion at play here. [Derek thinking of mathematical proportions]

00:58

The ratio of tricks performed to phone numbers received is 1 to 3.

01:03

Whether he’s sticking just one trick…two tricks…three tricks, or more… [3 hands holding up 1, 2, and 3 fingers]

01:06

…the ratio is always the same.

01:08

We can solve this problem by turning our ratios into fractions.

01:12

A ratio of 1 to 3 can be written as the fraction one-third.

01:15

Now…we’re told that he got 81 phone numbers…that correlates to the denominator of our fraction.

01:20

In the numerator of our new fraction, we can just call the number of tricks “t.”

01:25

And from here…we can isolate the variable by clearing the denominator… and then simplify. [Fractions of Derek's tricks and ratio]

01:30

81 times 1 is…81…and 3 times t is 3t.

01:35

So…3t equals 81. That's our equation.

01:40

Divide both sides by 3, and we get that t equals 27.

01:45

So yeah… 27 awesome skateboard tricks results in 81 phone numbers. [Derek skateboarding and girls watch]

01:50

Which seems like a really good deal…until that first Verizon bill winds up in Mom’s hands… [Derek's Mom holding a phone bill and Derek looks surprised]

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