ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos

Word Problems with Percents 656 Views

Share It!

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

Subjects:

Ratios, Percentages, and Proportions / Percents

Common Core Standards:

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.
Full Transcript