Explanation for Question 17 From the Math (Calc) Section on the Official Sat Practice Test 9
Question 17 reads if two w plus 40 is equal to 14 2 and four w plus five T is equal to 25. 3 What is the value of two w plus three T. 4 Okay. So for this one, you see that we have a system of equations. 5 Let's just write that out. We have two w plus four T is equal 6 to 14 and four w plus five 7 T is equal to 25. You can solve this system of equations 8 to find the values of Wnt using either elimination or substitution. 9 And for this time I'm going to use elimination. 10 So I'll multiply this top expression by two so that we can cancel out 11 that w term. 12 So that leaves us with four w plus eight T 13 is equal to 14. Times two is 28, 14 and then we have four w plus five T is equal to 25. 15 Now it's subtract the second equation from the first one. 16 And we have four w minus four, w is zero w 80 minus five 17 T is three T and 28 minus 25 is three. 18 So we have three T is equal to three T is equal to one. 19 And now we can just plug that T back into either one of the 20 expressions and solve from there. I'm just going to plug back into the first 21 one, which is two w plus four T because I'm drinking plugin T is 22 equal to one equals 14. 23 So that's two w plus four is equal to 14, 24 two w equals 10. 25 So w is equal to five. 26 Now the key here is that this is actually not what they're asking for. 27 It can be pretty common for people to just report the values of the 28 variables, such as w or T, 29 but that's not what they're asking for. They want two w plus three T 30 from us, so we can solve that pretty easily. 31 We have two w plus three T. 32 So if we know the values of Wnts, we have two times five plus 33 three times. One is equal to 10 plus three, 34 which is equal to 13. 35 So that's the answer choice C.