Topic A: Foundations
Identifying percent amount and base
We're asked to identify the percent, amount, and base in this problem. And they ask us 150 is 25% of what number? So another way to think about it is 25% times some number. So I'll do 25% in yellow. And 25% times some number is equal to 150. So the percent is pretty easy to spot. We have a 25% right over here. So this is going to be the percent. And we're multiplying the percent times some base number. So this right over here is the base. So we have the percent times the base. We have the percent times the base is equal to some amount. And you could try to solve this in your head. This is essentially saying 25% of some number, 25% times some number is equal to 150. If it helps, we could rewrite this as 0.25, which is the same thing as 25%. 0.25 times some number is equal to 150. And one interesting thing is just to think about, should that number be larger or smaller than 150? Well, if we only take 25% of that number, if we only take 25 hundredths of that number, if we only take 1/4 of that number, because that's what 25 hundredths is, or that's what 25% is, we get 150. So this number needs to be larger than 150. In fact, it has to be larger than 150 by 4. And to actually figure out what the number is, we can actually multiply. Since this, what's on the left-hand side is equal to the right-hand side, if we want to solve this, we can multiply both sides by 4. If we say, look, we have some value over here, we're going to multiply it by 4. In order for it to still be equal, we have to multiply 150 times 4. 4 times 0.25, or 4 times 25%, or 4 times 1/4, this is just going to be 1. And we're going to get our number is equal to 150 times 4 or it is equal to 600. And that makes sense, 25% of 600 is 150. 1/4 of 600 is 150.