## Wednesday, June 24, 2020

### SAT Math Using the Percentage Formula

Percentages can be surprisingly complicated on the SAT. Part of that is because we canÃ¢â‚¬â„¢t always translate them into fractions, which are easier to work with algebraically. While itÃ¢â‚¬â„¢s easy enough to think of 50% as , itÃ¢â‚¬â„¢s rarely so easy to make the conversion on the SAT, especially when the percentages given are, say, 35% or 15%. To make matters worse, the SAT wonÃ¢â‚¬â„¢t just test you on the simple process of finding the percentage of a number (like calculating a tip). Instead, itÃ¢â‚¬â„¢ll ask you to calculate in reverse (finding the whole from the part), find a combination of percentages, find a percent change, or give some other scenario-specific piece of information. The percentage formula Finding a percent is pretty easy, as long as you have a calculator. Just divide the part by the whole and multiply the decimal that comes out by 100. So if you ate 10 out of a serving of 12 buffalo wings, then you ate . Remembering that formula can save you some grief when you have to use it algebraically. Matt and two of his cousins ordered a plate of 24 buffalo wings at a restaurant. Matt ate x wings, while his cousin Laura ate half as many. If MattÃ¢â‚¬â„¢s cousin Alli ate four times as many wings as Laura, and the three together finished 87.5% of the wings, how many buffalo wings did Laura eat? 3 6 12 18 21 The first thing to do here is change that word problem into an algebraic expression. But letÃ¢â‚¬â„¢s make sure that equation is clear. On the left, we have the fraction of wings eaten. x+0.5x+2x represents the number that Matt and his cousins went through. x is MattÃ¢â‚¬â„¢s share, 0.5x (equal to half) is LauraÃ¢â‚¬â„¢s share, and 2x is what wing-lover Alli picked clean (since ). Divide that by the total number, and multiple by 100, and weÃ¢â‚¬â„¢ve followed the percentage formula. Then, itÃ¢â‚¬â„¢s just a matter of isolating x. And you can be sure that 6 is going to show up in our answer choices. BUT take a look at our question one more time. WhatÃ¢â‚¬â„¢s the number weÃ¢â‚¬â„¢re looking for? ThatÃ¢â‚¬â„¢s exactly the kind of trap the SAT might set up for you. The number of wings that Laura ate is half of x, which would be 3. Avoiding the formula ItÃ¢â‚¬â„¢s perfectly possible to avoid having to use the formula on a lot of SAT percentage questionsÃ¢â‚¬â€specifically, you can do that by plugging in some values. And if the answer choices donÃ¢â‚¬â„¢t have number values that you can test out? Check out this problem: A pair of shoes went on sale for a 40% discount. Then, in a clearance event, the reduced price was lowered once again by 25%. If the original price was x dollars, what was the final price in terms of x? You can still plug in, but youÃ¢â‚¬â„¢ll have to choose your own number to use for x. In this case, you want something thatÃ¢â‚¬â„¢s easy to take 40% of. WhatÃ¢â‚¬â„¢s the easiest number to get a percentage of? Try out either 10 or 100; I prefer the second. And 40% of 100 is 40, so after the first sale, the shoes were 60 bucks. Then, after 25% was taken off of that, they were 45 dollars. If you plug in x=100 to all of the answer choices, only one of them comes out to 45, and thatÃ¢â‚¬â„¢s answer choice (C). While itÃ¢â‚¬â„¢s good to know the percentages formula, remember that you donÃ¢â‚¬â„¢t usually need formulas on SAT math that arenÃ¢â‚¬â„¢t given to you in the beginning of the section.