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# Percent word problem: penguins

CCSS.Math:

## Video transcript

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 number of the total number of penguins who live at the zoo 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 0.3 0 times X times X is equal to is equal to 15 and now to solve this we just have to divide 0.3 or we have to divide both sides by 0.3 0 that zero point three zero zero point three zero we get X is equal to 15 divided by zero point three zero now that's let's let's do a little we're going to do a little arithmetic to solve this one so if we take zero it's 15 divided by zero point three zero so just as a refresher of dividing decimals we can 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 get for an answer but if you multiply both of them by 100 you move this decimal 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 1500 is a number of times at point three zero will go into 15 so let's think about this let me rewrite 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 multiply the numerator and the denominator here by 100 which wouldn't change the value of the fraction so 30 goes into let's see doesn't go into one doesn't go into 15 it does go into 100 50 goes into 150 five times five times 30 is 150 subtract you get zero and then 30 goes into 0 zero times so this 30 goes into 15 hundred 50 times so this right over here is equal 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 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 hundred so it's equal to 30 for every hundred it's equal to 30 for every hundred 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 over 50 is the same thing as 30 over 100 so the total number of penguins are 50