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Ratios, Percentages, and Proportions Videos 55 videos

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Word Problems with Percents 658 Views


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Description:

If the value of a painting increases by 15 percent every year, what was it worth 5 years ago? Hold up: why would you want to sell it now? In a few more years, you could be a millionaire. Patience is key.

Language:
English Language

Transcript

00:00

Percents, a la Shmoop. Have you ever wanted a system you can use

00:00

to judge just about anybody’s performance? You’ve probably heard percents mentioned

00:00

during sporting events. Or seen them on your graded tests.

00:00

Just about any statistic can be expressed with a percentage.

00:00

Although some things really shouldn’t be expressed that way…

00:00

When you express something as a percent, you are really determining how much per every

00:00

100. The same way cents are a portion of a dollar,

00:00

percents are a portion of 100%. Suppose you answered 24 out of 25 questions

00:01

correctly on your test. You just like to wreck the curve for everybody,

00:01

don’t you? First we find out how many times 25 goes into

00:01

100. So we can multiply 25 by 4 to get our magical number of 100. Then we multiply 24

00:02

by 4, which equals 96. Congratulations! You got a 96% on your test.

00:02

Percents pop up just about anywhere you can imagine.

00:02

For example, money matters are often expressed using percents.

00:03

Here’s a hint: the percentages in credit card terms and conditions usually are not

00:03

on your side – the best APR’s come in small packages.

00:03

Even seemingly small percentage changes in the stock market can have massive real-world

00:04

effects. Percents are a key part of the language of

00:04

economics, and sometimes just thinking in percents helps people to make good financial

00:04

decisions. For example, even if an outfit is “totally

00:04

super cute” you probably shouldn’t buy it if it costs more than fifty percent of

00:06

your net worth. If you’re a sports fan, you’re used to

00:06

hearing percents all the time. <<Announcer voice>> “Jones is only shooting

00:06

27 percent from the field tonight.” Field goal and free throw accuracy in basketball,

00:07

batting averages in baseball, passing completion rates in football… are all expressed in

00:07

percents. We hope your knowledge of percents has now

00:08

been improved by at least 62%. In fact, you even look 62% smarter than when

00:08

we started… But wait… there’s more!

00:08

You know that rare, valuable painting you found in the attic?

00:12

The one of all the trees? Well, apparently some collectors really like trees, because

00:16

it’s now worth $45,055. That is some fancy foliage.

00:26

Thank goodness you didn’t uncover it five years ago and sell it back then.

00:31

Now that we mention it… how much could you have sold it for five years ago?

00:38

Well, the painting’s value is appreciating annually by 15%.

00:47

So… how much would it have been worth half a decade earlier?

00:54

A - $10,265 B - $19,990

00:56

C - $21,780 D - $22,400

00:57

or E - $34,210? First, we’re going to need to pull a variable

01:02

out of our bag of tricks. Let’s make “V” the value of the painting

01:09

five years ago. Because we have the appreciated value and

01:13

want to find the original value, we should set our equation like this:

01:18

45,055 equals V times one plus point-one-five to the fifth.

01:24

Whoa – how did we get there? Well, the value of the painting increases

01:29

by 15% every year… …which is the “one plus point-one-five.”

01:34

The value is multiplied by that amount – one-point-one-five – for every year that passes.

01:41

So it’s the same as V times 1.15 times 1.15 times 1.15 times 1.15 times 1.15.

01:53

Okay, but our V is crowded with a whole mix of junk on the right side of the equation.

02:02

We want to get it by itself, so we can reconfigure the equation to look like this:

02:06

V equals 45,055 divided by 1.15 to the fifth. Then it’s simply a matter of doing the math…

02:30

or politely asking your calculator to do it for you

02:32

. Implore your calculator to first take 1.15

02:39

to the fifth… ...and then divide 45,055 by that result.

03:00

So looks like V equals $22,400.29. After dropping those 29 cents into your math

03:11

teacher’s tip jar, it appears our answer is option D.

03:18

Wow – it’s already worth nearly $23,000 more than it was five years ago!

03:22

At this rate, you’ll be able to retire in a few decades.

03:26

Assuming your future kids don’t one day try to add a few more trees.

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