[Video] Q29: A photocopy machine is initially loaded with 5,000 sheets of paper. the machine starts a large job and copies at a constant rate. after 20 minutes, it has used 30% of the paper. which of the following equations models the number of sheets of paper, p, remaining in the machine m minutes after the machine started printing?

Explanation for Question 29 From the Math (Calc) Section on the Official Sat Practice Test 8

So question number 29 tells us about a photocopy machine. 2 If we read this question, we can see that we start off with 5,000 3 sheets of paper, which makes sense, because in all of our answers, 4 we're also starting off with 5,000 sheets of paper. 5 And then if we look closely, we can see that we start a job 6 and then we make copies at a constant rate. 7 And whenever we see constant rate, our best bet is to think about a 8 linear graph. And then it says after 20 minutes, 9 it is used up 30% of the paper. 10 So now you've probably received conflicting signals. 11 You see 30%, which is usually an exponential growth 12 rate thing. Like when you put money in a bank and it grows by 13 an interest rate of 30%, but you've also seen constant rate. 14 And so we need to ask ourselves, is this linear or is this non-linear 15 and it's going to be linear, right? 16 Because sure we have the constant rate, 17 but it tells us after 20 minutes, we've used 30% of the paper. 18 And so that doesn't necessarily mean that you're changing by 30% every time. 19 But if we multiply 0.3 times 5,000, 20 we get 1500 right. 1500 pages. 21 So all that 30% means is this there to trick you because we could 22 rewrite it. It's just saying that in the first 20 minutes, 23 we've used 1,500 sheets of paper. 24 It doesn't have to be expressed as a percent. So it's this constant rate 25 that tells us that it has to be a linear function. 26 So it can only be either a or B. So now the question is, 27 do I do 20 pages a minute? Can I print 20 pages per minute? 28 Are my printing 75? And this is where that 20 minutes again comes in 29 handy because I know that I printed fifth per 1,500 pages 30 in 20 minutes. So if I take that number 1,500 and I divide by 31 20, I'll get the number of pages that I printed in one minute. 32 When I do that, I get 75. 33 So our starting 500, we're losing 75 pages per minute. 34 And so our correct answer is going to be B.