Percent word problems
Another Percent Word Problem Finding the full price when you know the discount price
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- Let's say I go to the fruit store today and they
- have a sale on guavas.
- Everything is thirty percent 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 six 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 six guavas, they charge me, I get the thirty percent off.
- They charge me $12.60.
- $12.60.
- So this is the thirty percent off sale price on six guavas.
- I go home, and then my wife tells me, you know, Sal, can
- you go get two more guavas tomorrow?
- I say, sure.
- So the next day I go and I want to buy two more guavas.
- So, two guavas.
- But now the sale is off.
- There's no more thirty percent.
- That was only that first day that I bought the six.
- 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 six 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 six guarvas.
- six guavas, at full price.
- So, essentially, if we take thirty percent off of this,
- we should get $12.60.
- So let's do that.
- So if we have the full price of six guavas, we're going
- to take thirty percent 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 thirty percent 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 thirty percent off of the full price.
- And now we just do algebra.
- We could imagine there's a one in front -- you know, x
- is the same thing as onex.
- 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, seventy percent of the full price is equal to
- my sale price, right?
- I took thirty percent off.
- This is seventy percent 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 ten, 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 seven, not a .seven.
- So seven goes into twelve one time.
- one times seven is seven.
- twelve minus seven is five.
- Bring down the six.
- seven goes into fifty-six eight times.
- eight times seven is fifty-six.
- And then we have no remainder.
- So it's eighteen, and there's nothing behind the decimal point.
- So it;s eighteen, in our case, $eighteen.
- So x is equal to $eighteen.
- Remember what x was? x was the full price of six guavas.
- x was the full price of six.
- x is the full price of six guavas.
- Now, the question is, how much will two guavas cost
- me at the full price?
- Well, this is full price of six.
- So you immediately could figure out what's the
- full price of one guava.
- You divide eighteen by six.
- So eighteen divided by six is $three.
- That's $three per guava at full price.
- And they're asking us, we want two guavas.
- So two guavas is going to be two times $three, so this
- is going to be $six.
- $six.
- Another way you could have done it, you could have just said,
- hey, six at full price are going to cost me $eighteen.
- two is one / three of six.
- So one / three of $eighteen is $six.
- So, just to give a quick review what we did.
- We said the sale price on six guavas, $12.60.
- That's thirty percent off the full price.
- Or you could say this is seventy percent of the full price.
- seventy percent of the full price.
- And so you could say, thirty percent -- so if you say x is the full price
- of six guavas, you could say the full price of six 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 six guavas, is $eighteen, or that's $three per guava or $six for two.
- Anyway, hopefully you found that helpful.
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