Explanation for Question 38 From the Math (Calc) Section on the 2020 October Sat
So 38 is kind of a funky looking question because it's asking us for 2 the product of two, two parentheses values, 3 two quantities that are just not used or just something that you're probably not 4 used to seeing. But if we look into our equation, 5 we can see that these quantities are already set up for us. 6 We have the one 30 plus five right here, 7 and then we have the one half year minus four, all right here. 8 And so something that we can do, that's actually pretty useful in a lot 9 of different disciplines of math. As we can pretend that these large quantities are 10 simpler variable, we can pretend that this one that I've highlighted in pink is 11 a, and this one that I've highlighted in yellow is B. 12 And since all the things in yellow and all the things in pink are 13 exactly the same. I'm going to rewrite these two equations, 14 but I'm going to use a and B instead of the crazy numbers and 15 variables that they have right now. 16 So I'll do a plus B is equal to 37. 17 They'll do a minus B is equal to 19. 18 Now this is a systems of equations that you're probably much more comfortable seeing. 19 What we can do is we can take this bottom equation and solve it 20 for a, and I get 19 plus these equal to eight, 21 and then I can take this and plug it back into my first first 22 equation is that 19 plus B plus B is equal to 37. 23 Now, when I combine like terms here, I get 19 plus two B is 24 equal to 37. And if I'm solving for B, 25 I can subtract 19. And then I get...
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