- Solving percent problems
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- Percent word problem: magic club
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- Percent word problem: guavas
- Discount, markup, and commission word problems
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.
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.