Identifying percent amount and base

we're asked to identify the percent amount and base in this problem and they asked us 150 is 25% of what number so another way to think about it is 25% 25% times some number so I'll do 25% in yellow and 25% times some number times number times some number is equal to is equal to 150 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 that is 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 is equal to is equal to some 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 can rewrite this as as 0.25 which is the same thing as 25% 0.25 times some number times some number is equal to 150 and what an interesting thing is just 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 hundred 50 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 percent or 4 times 1/4 worth this is just going to be one that is just going to be one and we're going to get our number is equal to 150 times four or it is equal to 600 and that makes sense twenty-five percent of 600 is 150 1/4 or 600 is 150