Percent word problem examples

In a video game, Val scored 30 percent fewer points than Peta. Peta scored 1060 points. How many points did Val score? Pause this video and see if you can figure out how many points Val scored.

All right, well now let's do this together, and there's a couple of ways that you could think about it. One way to think about it is Peta scored 1060 points, and Val scored 30 percent fewer. When we're saying 30 fewer, we're saying essentially take 30 percent of 1060 and subtract that from 1060.

So, 30 percent, so that we could write that as a decimal, is 0.30. Thirty hundredths is the same thing as thirty percent, or we could even write this as point three. Then we would want thirty percent of ten sixty. So if you take Peta's score and then subtract thirty percent of Peta's score, then this would give you Val's score.

So that's one way to calculate it. Another way to think about it is whatever you're starting with, let's call that 100. If you were to take out 30 percent of it, if you were to have 30 percent less, then you're going to have 70 percent of what you started with.

So another way to think about it is we could take Peta's score of 1060 and multiply it by 70 percent. Multiplying it by 70 is the same thing as multiplying it by 0.70, which is the same thing as multiplying it by 70 hundredths, the same thing as 7 tenths.

So let's just do this. If I have 1060 and I multiply by 0.7, what do I get? 7 times 0 is 0. 7 times 6 is 42. 7 times 0, 0 plus 4 is 4. 7 times 1 is 7, 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 percent more goblins than wizards in a magic club. There are 220 goblins and wizards altogether in the 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 going to involve a little bit of algebra here. What we want to 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. 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 more information. They tell us there are 20—let me box that—there are 20 percent more goblins than wizards.

So we also know one other thing: we know that the goblins are equal to the number of wizards plus 20 percent. You could view this as wizards plus 20 of wizards. I'm writing that as 20 hundredths, or you could even write that as two-tenths, plus two-tenths 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 two-tenths of that something, then I'm going to 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. Then we could say the number of wizards plus the number of goblins, which happens to be 20 percent more than the number of wizards, is going to be equal to 220.

Let me do that in the 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 use this as 1W plus 1.2W is equal to 2.2W, which 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, and that makes sense. 120 is 20 more than 100.

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 percent 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 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 percent, which you could say is 10 hundredths, or we could even say that as one-tenth.

He's one-tenth taller, so whatever his height was last year, we're going to add a tenth 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 a tenth of an X is going to be one and one-tenth X 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 want to do is move this; 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 1650 is.

And so let's see, let me just do that step by step. 11 goes into 16 one time. 1 times 11 is 11. Subtract, we get a 5, and we bring down a 5. 11 goes into 55 exactly 5 times. 5 times 11 is 55. Subtract, we have no remainder, but then we bring down this 0 and we do it one more time.

11 goes into 0; 0 times. Remember, the decimal place is right over here. 0 times 11 is 0, 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, 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 percent of that. 10 of 150 is 15 centimeters, so you add 10 percent of that. You indeed do get to 165 centimeters for the first day of school this year.