[Video] Q20: Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. the total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. which of the following represents the original price of the computer in terms of p ?

Explanation for Question 20 From the Math (Calc) Section on the Official Sat Practice Test 1

So here we see the, almost gotten a discount, 2 right? And we're trying to find what her starting price was. 3 The original price we'll call that S for starting price. 4 And we know that she got a 20% discount, 5 right. But we notice everything here has to do with 0.8. 6 And so the reason we don't do 0.2 times a times S is 7 because when you take a 20% discount off your left to pay 80% 8 of the price, right? So if you take 0.8 times the starting price, 9 that is what she paid, but it's not all, 10 but she paid because she also paid the tax, 11 right. She paid an 8% tax. 12 And when you're paying a tax, you pay 1.08 times 13 all of this, right? Because you're still paying for the whole thing. 14 So that's where the one comes in because you have to pay your original 15 starting amount. 16 You're paying an additional 8%. 17 So that's why the point is your eight comes after the one. 18 So when I multiply 1.08 times 0.8, 19 ES it gives me my starting point 0.8 S plus a little more plus 20 the 0.08. And that is equal to P right? 21 But I'm solving for S I want to get rid of P and the 22 way that I do that is by dividing both sides first by 1.08, 23 right. That way, these cancel. And that will give me 0.8 S is equal 24 to P over 1.08. But the 0.8 is still in the way as well. 25 Right? So I need to divide by 0.8. So I'll divide by 0.8 26 and that'll give me the S is equal to P over 1.8 27 1.08 times 0.8, 28 which will lead us to answer choice D.