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Video: Finding the Percent of a Quantity with Simple Fractions and Integers

Tim Burnham

Nancy earned $299 last month translating 2 documents. Given that 20% of the money she earned was from translating the second document, which of the following is the closest to the amount of money Nancy earned from translating the second document? [A] $30, [B] $60, [C] $270, [D] $279, [E] $290.

02:13

Video Transcript

Nancy earned two hundred and ninety-nine dollars last month translating two documents. Given that twenty percent of the money she earned was from translating the second document, which of the following is closest to the amount of money that Nancy earned from translating the second document? Is it A) thirty dollars, B) sixty dollars, C) two hundred and seventy dollars, D) two hundred and seventy-nine dollars, or E) two hundred and ninety dollars?

So first a quick analysis of the question then. so last month, Nancy earned two hundred and ninety-nine dollars and she translated two documents. Twenty percent of the money that she earned was from translating the second document. So the actual calculation if we were to do this accurately will be to find twenty percent of two hundred and ninety-nine dollars.

But we’re not asked to do the exact calculation. This is a kind of estimating question because we’ve just got to find out which is the closest answer. So couple of ways of approaching this, first of all twenty percent means a fifth of something, and two hundred and ninety-nine dollars is approximately equal to three hundred dollars.

Now this calculation, a fifth of three hundred, is something we can do pretty easily, and it’s gonna be pretty close to the right answer to the original question. So a fifth of three hundred is the same as three hundred divided by five. Well thirty divided by five would be six; six times five is thirty. So three hundred times divided five is gonna be sixty.

So our estimate of the answer, but in fact that estimate is gonna be a slight overestimate. We actually want to know twenty percent of two hundred and ninety-nine not twenty percent of three hundred. But nevertheless it’ll be pretty close, so let’s look through our answers that we were given: thirty dollars, sixty dollars, two hundred and seventy dollars, two hundred and seventy-nine dollars, two hundred and ninety dollars. Sixty dollars, there we go, it’s B!

Now although we said sixty dollars was an overestimate, it’s only a very slight overestimate. So there’s no way that thirty dollars is gonna be closer to the right answer; it’s gonna be very close to sixty dollars.