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### 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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# Solving percent problems

We'll use algebra to solve this percent problem. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- The way I thought of it was that you multiply 150 times 4, knowing that 25% is 1/4 of 100% soooo by doing this we would find the number that 150 would be 25% of. Is this right and did I confuse anyone? It was just the simplest way I thought of it(55 votes)
- @edgel- I did that, and I like that way because it's fast but @Crystallized_Pineapple is also right(2 votes)

- Why can't You Just Do This~ (for the first Part) ;

150 is 25% of what number?:**25% is part of a whole 100%.***.

*25% is 1/4 of 100%*

so, you know that (150) is 1/4 of the answer(100%)

Add 150 - 4 times (*Because we know that 25% X 4 = 100%*)

And that is equal to: (*150 + 150 + 150 + 150*) = *600

The method they used in the video is also correct, but i think that this one is easier, and will make it more simple to solve the rest of the question.(33 votes)- You can use that method, as long as the answer matches the same one as the other method's answer. If you find it to be easier then there is no reason not to use it, unless your math teacher requires a different method.(6 votes)

- for example : 92% of a number is 56. how would i do this?(11 votes)
- There are 2 methods.

1) Translation. The word "of" means multiply. The word "is" means "=". Translate: 92% of a number is 56

You get: (92/100)x = 56 or as decimals 0.92x = 56

Then solve for x.

2) Proportion method. You will often see this described as "is" over "of" = "percent" over 100. The number associated with "is" in your problem is the 56. The number associated with "of" is the unknown value, so use "x". The "percent" is the 92%. This give you the proportional equation: 56/x = 92/100. You can cross-multiply, then divide to solve for x.

Hope this helps.(10 votes)

- i dont understand, how does this relate to the exercise questions?(14 votes)
- why cant you just change the 25% into decimal and the just divide with 150(8 votes)
- If you mean do 150 divided by 0.25, that's essentially what he did, but he explained it more.(7 votes)

- Unfortunately, I didn't find this video helpful.(11 votes)
- bro this doesnt help me in exercises after this(7 votes)
- At3:18, how do you do what he's doing?(4 votes)
- Do you know how division equations are the same thing as fractions? Well if you do then he converted the division equation into a fraction, so it will look like this 150/.25 but then he added a decimal and 2 zeroes after the decimal on the 150 so now the fraction was like this 150.00/.25 As you know the value doesn't change. Now in fractions, if you do the same thing to both the numerator and the denominator then the fraction can still be equivalent. So he moved the decimal 2 places to the right making the fraction 15000/25. After he did that he converted the fraction back into a division equation, and now he got 15000÷25 = ___. Hope this helped!(4 votes)

- how do a solve a problem like this in a proportion form?(6 votes)
- A hockey set is coming for $7 and there is 25% off. What is the price of the hockey set with the discount?

I got the answer as $5.25. Did I get it right(4 votes)

## Video transcript

We're asked to identify the
percent, amount, and base in this problem. And they ask us, 150 is
25% of what number? They don't ask us to solve it,
but it's too tempting. So what I want to do is first
answer this question that they're not even asking
us to solve. But first, I want to answer
this question. And then we can think about what
the percent, the amount, and the base is, because
those are just words. Those are just definitions. The important thing is
to be able to solve a problem like this. So they're saying 150 is
25% of what number? Or another way to view this,
150 is 25% of some number. So let's let x, x is equal
to the number that 150 is 25% of, right? That's what we need
to figure out. 150 is 25% of what number? That number right here
we're seeing is x. So that tells us that if we
start with x, and if we were to take 25% of x, you could
imagine, that's the same thing as multiplying it by 25%, which
is the same thing as multiplying it, if you
view it as a decimal, times 0.25 times x. These two statements
are identical. So if you start with that
number, you take 25% of it, or you multiply it by 0.25, that
is going to be equal to 150. 150 is 25% of this number. And then you can solve for x. So let's just start with
this one over here. Let me just write it separately,
so you understand what I'm doing. 0.25 times some number
is equal to 150. Now there's two ways
we can do this. We can divide both sides of this
equation by 0.25, or if you recognize that four quarters
make a dollar, you could say, let's multiply both
sides of this equation by 4. You could do either one. I'll do the first, because
that's how we normally do algebra problems like this. So let's just multiply
both by 0.25. That will just be an x. And then the right-hand side
will be 150 divided by 0.25. And the reason why I wanted to
is really it's just good practice dividing
by a decimal. So let's do that. So we want to figure out what
150 divided by 0.25 is. And we've done this before. When you divide by a decimal,
what you can do is you can make the number that you're
dividing into the other number, you can turn this into
a whole number by essentially shifting the decimal
two to the right. But if you do that for the
number in the denominator, you also have to do that
to the numerator. So right now you can view
this as 150.00. If you multiply 0.25 times
100, you're shifting the decimal two to the right. Then you'd also have to do
that with 150, so then it becomes 15,000. Shift it two to the right. So our decimal place
becomes like this. So 150 divided by 0.25
is the same thing as 15,000 divided by 25. And let's just work it
out really fast. So 25 doesn't go into 1, doesn't
go into 15, it goes into 150, what is that? Six times, right? If it goes into 100 four
times, then it goes into 150 six times. 6 times 0.25 is-- or actually,
this is now a 25. We've shifted the decimal. This decimal is sitting
right over there. So 6 times 25 is 150. You subtract. You get no remainder. Bring down this 0 right here. 25 goes into 0 zero times. 0 times 25 is 0. Subtract. No remainder. Bring down this last 0. 25 goes into 0 zero times. 0 times 25 is 0. Subtract. No remainder. So 150 divided by 0.25
is equal to 600. And you might have been able
to do that in your head, because when we were at this
point in our equation, 0.25x is equal to 150, you could
have just multiplied both sides of this equation
times 4. 4 times 0.25 is the same
thing as 4 times 1/4, which is a whole. And 4 times 150 is 600. So you would have gotten
it either way. And this makes total sense. If 150 is 25% of some number,
that means 150 should be 1/4 of that number. It should be a lot smaller than
that number, and it is. 150 is 1/4 of 600. Now let's answer their
actual question. Identify the percent. Well, that looks like 25%,
that's the percent. The amount and the base
in this problem. And based on how they're wording
it, I assume amount means when you take the 25% of
the base, so they're saying that the amount-- as my best
sense of it-- is that the amount is equal to the percent
times the base. Let me do the base in green. So the base is the number you're
taking the percent of. The amount is the quantity
that that percentage represents. So here we already saw
the percent is 25%. That's the percent. The number that we're taking
25% of, or the base, is x. The value of it is 600. We figured it out. And the amount is 150. This right here is the amount. The amount is 150. 150 is 25% of the
base, of 600. The important thing is how
you solve this problem. The words themselves, you know,
those are all really just definitions.