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## 7th grade

### Unit 3: Lesson 3

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: guavas

CCSS.Math:

We're putting a little algebra to work to find the full price when you know the discount price in this percent word problem. Created by Sal Khan.

## Video transcript

Let's say I go to the fruit
store today and they have a sale on guavas. Everything is 30% off. This is for guavas. And it's only today. Only today. So I say, you know what, let
me go buy a bunch of guavas. So I go and I buy 6 guavas. So I buy six guavas. And it ends up, when I go to
the register, and we're assuming no tax, it's a grocery
and I live in a state where they don't tax groceries. So for the 6 guavas, they
charge me, I get the 30% off. They charge me $12.60. $12.60. So this is the 30% off
sale price on 6 guavas. I go home, and then my wife
tells me, you know, Sal, can you go get 2 more
guavas tomorrow? I say, sure. So the next day I go and I
want to buy 2 more guavas. So, 2 guavas. But now the sale is off. There's no more 30%. That was only that first
day that I bought the 6. So how much are those two
guavas going to cost me? How much are those two guavas
going to cost at full price? At full price? So, a good place to start
is, to think about how much would those 6 guavas have
cost us at full price? This is the sale
price, right here? This is the sale price. How much would those have
cost me at full price? So let's do a little
bit of algebra here. Pick a suitable color
for the algebra. Maybe this grey color. So, let's say that x is equal
to the cost of 6 guarvas. 6 guavas, at full price. So, essentially, if we
take 30% off of this, we should get $12.60. So let's do that. So if we have the full price
of 6 guavas, we're going to take 30% off of that. So that's the same
thing as 0.30. Or I could just write 0.3. I could ignore that
zero if I like. Actually, let me
write it like this. My wife is always bugging me to
write zeroes before decimals. So that's the full price of
6 guavas minus 0.30 times the full price of guavas. Some I'm just taking 30%
off of the full price, off of the full price. This is how we figure
out the sale price. This is going to be equal to
that $12.60 right there. That's going to be
equal to $12.60. I just took 30% off
of the full price. And now we just do algebra. We could imagine there's a
1 in front -- you know, x is the same thing as 1x. So 1x minus 0.3x is going
to be equal to 0.7x. So we get 0.7x, or we could
say 0.70 if you like. Same number. Point, or 0.7x, is
equal to 12.60. And once you get used to these
problems, you might just skip straight to this
step right here. Where you say, 70% of the
full price is equal to my sale price, right? I took 30% off. This is 70% of the full price. You might just skip to this
step once you get used to these problems in a little bit. And now we just have
to solve for x. Divide both sides by 0.7,
so you get x is equal to 12.60 divided by 0.7. We could use a calculator, but
it's always good to get a little bit of practice
dividing decimals. So let's do that. So we get 0.7 goes into 12.60. Let's multiply both of these
numbers by 10, which is what we do when we move both of their
decimals one to the right. So the 0.7 becomes a 7. Ignore that right there. The 12.60 becomes 126, put
the decimal right there. Decimal right there. And we're ready to just do
straight up long division. So this is now a 7, not a .7. So 7 goes into 12 1 time. 1 times 7 is 7. 12 minus 7 is 5. Bring down the 6. 7 goes into 56 8 times. 8 times 7 is 56. And then we have no remainder. So it's 18, and there's nothing
behind the decimal point. So it;s 18, in our case, $18. So x is equal to $18. Remember what x was? x was
the full price of 6 guavas. x was the full price of 6. x is the full price
of 6 guavas. Now, the question is, how
much will 2 guavas cost me at the full price? Well, this is full price of 6. So you immediately could
figure out what's the full price of one guava. You divide 18 by 6. So 18 divided by 6 is $3. That's $3 per guava
at full price. And they're asking us,
we want 2 guavas. So 2 guavas is going to
be 2 times $3, so this is going to be $6. $6. Another way you could have done
it, you could have just said, hey, 6 at full price are
going to cost me $18. 2 is 1/3 of 6. So 1/3 of $18 is $6. So, just to give a quick
review what we did. We said the sale price
on six guavas, $12.60. That's 30% off the full price. Or you could say this is
70% of the full price. 70% of the full price. And so you could say, 30% -- so
if you say x is the full price of 6 guavas, you could say the
full price of 6 guavas minus 30% of the full price of 6
guavas is equal to 12.60, and that's equivalent to saying,
70% of the full price is 12.60. You divided -- then we just
solved this algebraically. Divide both sides by 0.7, and
then we got x, the full price of 6 guavas, is $18, or that's
$3 per guava or $6 for 2. Anyway, hopefully you
found that helpful.