If a – (b/3) = 1/3 and a + (b/4) = 3/2, then what is the value of a + b? A. 1 B. 2 C. 3 D. 4 E. 5
(C) Whenever we have fractions in algebra, it is usually a good idea to eliminate them. Let’s multiply the first equation by 3, yielding:3a – b = 1.Then let’s multiply the second equation by 4, yielding:4a + b = 6. If we add the equations, the b terms cancel out, yielding: (3a – b = 1) + (4a + b = 6) 7a = 7 a = 1.
Now, we can substitute the value of a into either of the equations to determine that b = 2.Therefore, a + b = 1 + 2 = 3.The correct answer is choice (C).
If we add the equations, the b terms cancel out, yielding: (3a – b = 1) + (4a + b = 6)
7a = 7 a = 1
My question is how do you know when you should be adding equations together (The step referenced above). I know there has to be a fundamental concept I am forgetting. I think I tried the solving for a and then substituting the answer into the other equation, therefore treating each equation as if they are mutually exclusive. Please explain the correct approach/rationale and how to make the correct determination. Thanks.
