Percentage word problems
A zoo has 15 emperor penguins who make up 30% of the total number of penguins at the zoo. How many penguins live at the zoo? So let's let x equal the total number of penguins who live at the zoo. So they're telling us that 30% of that are the emperor penguins, which are 15. So they're saying if we take 30%, so 30% of x is equal to 15. Or another way of saying this is we could say, Instead of writing 30%, we could write that as a decimal, as 0.30 of x. So it's 0.30 times x is equal to 15. And now to solve this, we just have to divide both sides by 0.30. So let's do that. 0.30, 0.30, we get x is equal to 15 divided by 0.30. We're going to have to do a little arithmetic to solve this one. So if we take 0-- it's 15 divided by 0.30. So just as a refresher of dividing decimals, we could essentially multiply both of these by 100. And when you multiply both of them by 100, you can't just multiply one of them. Then you would get a different answer. But if you multiply both of them by 100, you move this decimal point over two spots, so it becomes a 30. And you move this decimal over two spots, so it becomes 1,500. So it really boils down to how many times-- the same number of times that 30 goes into 1,500 is the number of times that 0.30 will go into 15. So let's think about this. Let me rewrite it here, just so it's neat. 30 goes into 1,500, all we did is we moved both decimals over to the right twice. Or you could say we just multiplied the numerator and the denominator here by 100, which wouldn't change the value of the fraction. So 30 goes into-- let's see, it doesn't go into 1. It doesn't go into 15. It does go into 150. It goes into 150 five times. 5 times 30 is 150. Subtract, you get 0. And then 30 goes into 0 zero times. So this 30 goes into 1,500 fifty times. So this right over here is equal to 50. And you can verify it. Multiply 0.3 times 50, and you will get 15. Now, there is another way of doing it. You could say the fraction of emperor penguins over the total number of penguins at the zoo. So you could say 15. You could say 15 over the total number of penguins at the zoo is equal to 30%. Percent literally means 30 hundreds. So it's equal to 30 for every 100. It's equal to 30 for every 100. And then you could solve for this right over here. And a really simple way of doing this is you say, look, to go from 30 to 15, you have to divide by 2 if you're going from the right to the left. So let's divide by 2 right over here. So x would be equal to 50. 15/50 is the same thing as 30/100. So the total number of penguins are 50.