ID: 5910bfff
(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Advanced Math)
Comment: Back to basics.
Method 1: Isolate H, one step at a time. I have had high-level students who have missed this question because they have gone too fast and flipped a sign along the way in their head, without writing out a sufficient number of steps to ensure the answer is accurate.
D = T - (9/25)(100 - H)
D - T = -(9/25)(100 - H)
-(25/9)(D - T) = 100 - H
-(25/9)(D - T) - 100 = -H
(25/9)(D - T) + 100 = H
The correct answer is (A).
Method 2: You can use Desmos to graph the function, adding a slider for one of the variables, or as a calculator, picking numbers for, say, T and H. In the graph below, I will set T to 40.
This gives a y-intercept at 4. You can now plug in these values to the given equations in the answer choices and see which one yields H = 0. (Yes, the setup tells us that H > 50, but in this linear function, such information makes no difference.)
A. H = (25/9)((4) - (40)) + 100 --> H = (25/9)(-36) + 100 --> H = -100 + 100 --> H = 0 √
B. H = (25/9)((4) - (40)) - 100 --> H = (25/9)(-36) - 100 --> H = -100 - 100 --> H = -200 X
C. H = (25/9)((4) + (40)) + 100 --> H = (25/9)(44) + 100 --> H = 122 2/9 + 100 --> H = 222 2/9 X
D. H = (25/9)((4) + (40)) - 100 --> H = (25/9)(44) - 100 --> H = 122 2/9 - 100 --> H = 22 2/9 X
Since all other answer choices are eliminated, it is clear that the correct answer is (A).
Method 3: Similar to the above, you could choose values for T and H, perhaps even an H-value that conforms to the given information; derive D; then test each answer choice for equivalence. However, the algebraic method is probably best here.
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