We need an equation that tells us how many questions you will get right for every 10-minute period you study. This is a linear equation. Let’s call the number of equations you get right q and the number of study periods p. Then q depends on p. We start with 8 questions when there are no extra study periods, that is, when p=0, q=8. When p=1 (one 10-minute study period) q=10 so q=8+2p. With 2 study periods, q=8+4=12.

This is the equation q=8+2p. We could have used x for the number of study periods and y for the number of correctly answered questions. But q reminds us that we are talking about the number of questions and p the number of study periods.

Suppose we wanted to replace p with time t in minutes. For every 10 minutes q increases by 2 so we need to divide the time in minutes by 10 to get the number of study periods. So we replace p by t/10. Now the equation becomes q=8+2t/10 or q=8+t/5. So now we can test it by putting in a value for t. If t=10 we get q=10. And we get q=9 if t=5. But this is a new fact that may not be true. A 5-minute study period means that we can correctly answer one question. But is that what the words in the question mean? And if t=3 we get a number containing a fraction for q. So we may need to add constraints to the values of t. Anyway, you can see the math I hope by now and take on board what the implications of the equation are.

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