Explanation for Question 21 From the Math (Calc) Section on the Official Sat Practice Test 10
So now we're looking at question number 21, 2 which says that point 10 X plus 0.2 Y is equal to point 18 3 times X plus Y. Then it tells us that Clayton's going to mix T 4 X milliliters of a 10% saline solution. 5 So that X of a 10% is where we get this term from where 6 the Y mill the milliliters of a 20% set mass St lean solution in 7 order to create a total of 18% massively solution. 8 And it says that this equation above represents the situation, 9 right? So if Clayton is going to use 100 milliliters of the 20% by 10 mass saline solution, how many milliliters of the 10% must 11 he use? So first we see that the Y is the 20% by mass 12 solution. And we're going to use 100 milliliters of that. 13 So wherever we see a Y we should just plug in 100 milliliters or 14 just 100 would be okay, right? 15 So we have zero point 10 X plus 0.2 times 100 is 16 equal to 18 plus times X plus 100, 17 right? And there's a little bit of simplifying we can do starting right here. 18 It says point 10 X plus 0.2 times 100 that's 20 19 is equal to, and we'll distribute right here. 18 point 20 18 point 18 X plus point 18 times a hundred 21 is 18. And so now we simply need to solve for X, 22 right? And we can do that by moving all our X terms over to 23 one side and all of our normal terms over to the right. 24 So I'll subtract point 10 X from both sides so that I get 0.08 25 X plus 18 is equal to 20, 26 and I want to move this 18 over to the other side, 27 get away from my ex. So those will cancel. 28 And I get to, as he goes, you're a 0.08 X now to solve 29 for X. My last step is going to be to divide by 0.08. 30 And if I do two divided by 0.08, 31 plug that in my calculator get that 25 is equal to X. 32 And we see that here in answer choice B yep. 33 Just double-checking he was asking, or the test tape test maker was acne 34 asking how many milliliters of the 10% solution should we use? 35 And the 10% solution is in fact denoted by X. 36 So our correct answer is B.