Algebra Equations: Substitution

Read the following SAT test question and then select the correct answer. 

For every SAT math problem, read the problem carefully so that you know exactly what information you are given.  Then identify the bottom line, the information that you must find.  Assess your options for solving the problem, and choose the most efficient method to get to the answer.  Attack the problem to find the answer, and loop back to your bottom line to make sure that your answer matches what you were supposed to find.

If   and x = 12, then x – y =

Bottom Line: x – y = ?

Assess your options:  You could try to work backwards from the answer choices, but that would require you to know the values for x and y.  Instead, use arithmetic to solve for x and y, then plug those numbers into the last equation to find the bottom line.

Attack the problem: You are given the fact that x = 12.  You can create another equation to solve for x: if you multiply both sides of the first equation by y, you have x = 3y. Now plug in your x value and you will have 12 = 3y. When you divide both sides by 3, you will find that 4 = y.  Return to the last equation and plug in your values for x and y: x – y becomes 12 – 4 = 8.

Loop back: The last equation was your bottom line, so you are ready to look at the answer choices.

(A)  3

(B)  5

(C)  6

(D)  8

(E)  9

The correct answer is (D).

On sat.collegeboard.org, 78% of the responses were correct.

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