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## Pre-algebra

### Course: Pre-algebra > Unit 8

Lesson 1: Percent word problems- Solving percent problems
- Equivalent expressions with percent problems
- Percent word problem: magic club
- Percent problems
- Percent word problems: tax and discount
- Tax and tip word problems
- Percent word problem: guavas
- Discount, markup, and commission word problems

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# Percent word problem: magic club

Sal solves percent word problems including percent comparisons and percent of change.

## Want to join the conversation?

- Hi everyone

for example, Dave is 170cm tall, and Dave is 10% taller than mike. The same thing as Mike is 10% shorter than Dave?

Also, what exactly do they mean by Dave is 10% taller than mike. Does it mean he is taller by 10% of Mike’s height or 10% of Dave’s height?

I know it might seem easy but I somehow just can’t get over this question.

Thanks(47 votes)- In your example, Dave is 10% taller than Mike is the same as Mike * (1 + 10%) = Dave. Mike is 10% shorter than Dave is the same as Dave * (1 - 10%) = Mike. Therefore, the two are different things. In the first example, Dave's height depends on Mike's height. In the second example, Mike's height depends on Dave's height. (If you still have doubts, assign specific numbers to Dave or Mike's height and calculate whether the two statements result in the same heights)

Remember, in percent word problems like the one you just asked, when something is taller or shorter, bigger or smaller than another, the independent variable is always the object after 'than'. So the object before 'than' is calculated from the object after 'than'.

A better way to understand this is to use variables. Let Dave be d and Mike be m, the relationship between d and m in the first statement is d = (1 + 10%) * m.

Hope this helps. Feel free to comment below if you have any more questions.(64 votes)

- Hey guys! This is an easier way to calculate a percent word problem (I learnt it in my Marshall Cavandish book). Let's take the first question Sal solved. That is, in a video game, Val scored 30% fewer than Peeta. Peeta scored 1060 points.

So this is the method:

100% = 1060

1%= 10.6

70%= 10.6*70= 742

Therefore, Val scored 742 points.(49 votes) - How do the goblins equal to 1.2 times the wizards(19 votes)
- 20% more than implies you start with 100% and add 20% to this to get 120%. If you just stuck with 20%, that would assume there were 5 times as many wizards as goblins.(26 votes)

- I have analyzed this problem over and over and i have come up with the different result. I was confused on how u solved the problem because i perceived it the other way. And here is my solution:

220 = 100%

Goblin is 20% + 40% = 60%

Wizard is 40%

FOR THE GOBLINS

percent x base = amount

60% X 220 = amount

0.60 x 220 = 132 Goblins

FOR THE WIZARDS

percent x base = amount

40% x 220 = amount

0.40 x 220 = 88 Wizards

What is the 20% of 220?

percent x base = amount

20% x 220 = amount

0.20 x 220 = 44

What is the 10% of 220?

percent x base = amount

10% x 220 = amount

0.10 x 220 = 22

If Goblins and Wizards were EQUAL:

Divide the 20% of 220 by 2.

Goblins: 132-22 = 110

Wizards: 88+22 = 110

Why is this?

No matter how i analyse, i come up with this one which i believed is reasonable. Please explain why your solution is the correct one. Thank you!(19 votes)- Because when it says there is 20% more goblins than wizards you aren't looking for 20% of 220 more,

you are looking for

20% more than**the number of wizards**

hence-> goblins=wizards+wizards(0.2)

EDIT

so if you plug in your numbers,

goblins = 60% = 132

wizards = 40% = 88

To find 20% more goblins than wizards you would first have to find 20% of wizards (88) which would be...

-> 20% x 88 = 17.6

20% of 88**more**goblins would then equal

->88 + 17.6 =**105.6**

(not 132)

Just think about the question if you weren't given the information of 220 total. What would the expression be?

goblins = wizards + 20% of wizards(3 votes)

- why can't Sal just use fractions?
**120%=6/5**. I got my answer in 10 seconds for the goblins/wizards problem.3:51A kid I tutor was asking me about this question, but I find it easier to use fractions rather than decimals.

just a tip, no hate... khan academy is great(14 votes)- can you help me on the goblin problem i dont understand(12 votes)

- I don't quite understand the whole video at all. I've wtached the video many times but I'm still stuck in it.(15 votes)
- Yo bro just ask ya mama(4 votes)

*couldn't we just take 10% of 165 and then subtract it without any extra steps*(8 votes)- Because that is not what the word problem is asking. The word problem tells us that 165 is the
*ending*height and we need to calculate the*beginning*height. The problem also tells us that the ending height is 10% greater than the beginning height which is

10% of the ending height is*beginning height + beginning height * 10% = ending height***not**the same as 10% of the beginning height.(12 votes)

- i cant figure out how to set up an equation on equivalent expressions with percent problems!a tip or/and example or anything would help.thanks.(7 votes)
- at7:34isn't it 148.5(5 votes)
- The word problem tells us that 165 is the
*ending*height and we need to calculate the*beginning*height. The problem also tells us that the ending height is 10% greater than the beginning height which is

You can re-watch the video to see how Sal arrives at the answer, but lets take a look at what happens when we substitute the answers back into the original equation.*beginning height + beginning height * 10% = ending height*

or*beginning height + beginning height * 10% = ending height*

148.5 + 148.5 * 0.10 = ending height

148.5 + 14.85 = ending height

163.35 = ending height*beginning height + beginning height * 10% = ending height*

150 + 150 * 0.10 = ending height

150 + 15.00 = ending height

165 = ending height(4 votes)

- How do you do the Tax and tip word problems like:

Aubrey's dinner cost $85. She tips the waitstaff 30%. How much does Aubrey tip the waitstaff?

BTW I do not know what taxes and tips are(2 votes)- Percentages (%) mean out of 100. To find the percent of a certain amount, move the decimal point of the value with the percent sign toward the left twice (divide by 100), remove the percent sign, then multiply it by the initial amount.

$85*30%

$85*0.3

0.3=3/10

$85*(3/10)=$255/10

=25.5

There are a number of different ways to do this; for example, you could first turn 85 into 8.5 then multiply it by 3.**Taxes**(in Economics) are the primary source of revenue (source of money) for most governments. Taxes may be collected through income or purchases (often based on how much money is earned, spent, and perhaps different percentages for different products). Taxes are required by law if the government says so.**Tips**are an "additional/extra" payment given to waiters of a restaurant. Tips are not required, but a guest at a restaurant may give a tip (of money) if the waiter does well (e.g. in carrying the guest's food, the accuracy of the order, is not slow, etc.; this gives an incentive to the waiters to do well, perhaps performing better than what the restaurant requires).(9 votes)

## Video transcript

- [Instructor] In a video game, Val scored 30% fewer points than Peeta. Peeta scored 1,060 points. How many points did Val score? Pause this video and see
if you can figure out how many points Val scored. Alright, now let's do this together. And there's a couple of ways
that you could think about it. One way to think about is
Peeta scored 1,060 points, and Val scored 30% fewer. When we're saying 30% fewer, we're saying essentially take 30% of 1060 and subtract that from 1060. So 30%, so we could write
that as a decimal as 0.30. 30/100 is the same thing as 30%, or we could even write this as .3. And then we would want 30% of 1060. So if you take Peeta's score and then subtract 30% of Peeta's score, then this would give you Val's score. So that's one way to calculate it. Another way to think about is whatever you're starting
with, let's call that 100%, and if you were to take out 30% of it, if you were to have 30% less, then you're going to have
70% of what you started with. So another way to think about it is we could take Peeta's score of
1060 and multiply it by 70%. And multiplying it by
70% is the same thing as multiplying it by 0.70, which is the same thing as
multiplying it by 70/100, is the same thing as 7/10. So let's just do this. So if I have 1060, and I multiply by 0.7, what do I get? Seven times zero is zero. Seven times six is 42. Seven times zero is
zero, plus four is four. Seven times one is seven. And I have one digit to
the right of the decimal. So there you have it, it is 742. 742. That is how many points Val scored. Let's do another example. So we're told there are 20% more goblins than wizards in a magic club. There are 220 goblins and
wizards altogether in magic club. How many goblins are in the magic club? So pause the video and see if you can work through this on your own. So this one is an interesting one. It's gonna involve a
little bit of algebra here. So what we wanna do is
let's set a variable. Let's say w is the number of wizards. So that's the number of wizards. And then if we said g for
goblins, let's say g for goblins. So w plus g is equal to 220, is equal to 220. And you're like, well,
how does that help me? How does that help me actually figure out how many goblins are in the magic club? I have two variables
here with one equation. Well, one way to think about it is, remember, they give us
some more information. They tell us there are
20%, let me box that, there are 20% more goblins than wizards. So we also know one other thing. We know that the goblins,
we know that the goblins are equal to the number
of wizards plus 20%. So you could view this as wizards plus 20% of wizards. And I'm writing that as 20/100, or you could even write that as 2/10, plus 2/10 times the number of wizards. Or another way of thinking about it, goblins are equal to, if
I have one of something and then I have another
2/10 of that something, then I'm gonna have 1.2 of that something. So goblins is equal to
1.2 times the wizards. And so we could use that
to substitute back in here, and then we could say
the number of wizards plus the number of goblins,
which happens to be 20% more than the number of wizards,
is going to be equal to 220. Let me do that in that same color. Is equal to 220. Now this is pretty
straightforward to solve. What is w plus 1.2w? Well, that is going to be 2.2w, 2.2w. You could view this as one w plus 1.2w is 2.2w is equal to 220. And so just divide both sides. Let me scroll down a little bit. Divide both sides by 2.2, 2.2, and what do you get? You get w, the number
of wizards is equal to, let's see, this is going
to be equal to 100. The number of wizards is equal to 100. Now is that our answer? No, they're asking how many
goblins are in the magic club? Well, we know that goblins
are 1.2 times the wizards. So the number of goblins is
going to be 1.2 times 100, which is equal to 120. So there's 120 goblins,
does that make sense? 120 is 20% more than 100. And if you add the 100
wizards to the 120 goblins, you get 220 goblins
and wizards altogether. Let's do another example. Here we're told Cody
was 165 centimeters tall on the first day of school this year, which was 10% taller than he was on the first day of school last year. How tall was Cody on the
first day of school last year? Pause this video, see if
you can figure that out. So let's just define a variable here. Let's just say that his
height on the first day of school last year,
let's say that that is x. So his height on the first
day of school last year is x. This year he is 10% taller, so we would add 10%, which
we could say is 10/100, or we could even say that as 1/10. He's 1/10 taller. So whatever his height was last year, we're going to add 1/10
of that same height again to get to his height this year, which they tell us is 165 centimeters. And so here we could say
well, one x plus 1/10 of an x is going to be one and
1/10x is equal to 165. And now to solve for x, which
remember, was his height on the first day of school last year, we divide both sides by 1.1. And so x is equal to, well, let's see what this is going to be. If I were to take 165 divided by 1.1, the first thing I would wanna do is multiply them both by 10. So that has the effect of moving this decimal place one to the right. So really, I am now trying to figure out what 11 goes into 1,650 is. And so let's see, let me
just do that step by step. 11 goes into 16 one time. One times 11 is 11. Subtract, we get a five,
and we bring down a five. 11 goes into 55 exactly five times. Five times 11 is 55. Subtract. We have no remainder, but
then we bring down this zero and we do it one more time. 11 goes into zero zero times. Remember, the decimal
place is right over here. Zero times 11 is zero, and
then we have no remainder. So last year he was 150 centimeters. And it's always good
to do a reality check. Make sure, if for example,
if I divided wrong and I somehow got 15, or I got 1500, just to make sure that that
wouldn't make any sense. 150 centimeters, you add 10% of that. 10% of 150 is 15 centimeters. So you add 10% of that, you indeed do get to 165 centimeters for the
first day of school this year.