SAT Algebraic Manipulations

Correct Answer: E

Solution:

Tip: When distributing, be careful with signs!
$\begin{array}{r c l l} 32 &=& a ( b-c) &\quad \text{given}\\ 32 &=& ab - ac &\quad \text{use distributive property}\\ 32 + ac &=& ab &\quad \text{add}\ ac\ \text{to both sides}\\ 32 + 8 &=& ab &\quad \text{plug in}\ ac=8\\ 40 &=& ab &\quad \text{solve}\\ \end{array}$

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Incorrect Choices:

(A)
This wrong answer is the quotient of the two numbers that appear in the prompt.

(B)
Tip: Just because a number appears in the question doesn't mean it is the answer.
If $ab = 8$ , then $a(b-c) = ab - ac = 8 - 8 = 0$ , which is not equal to 32.

(C)
Tip: When distributing, be careful with signs!
You will get this wrong answer if you forget about the negative sign when distributing.
If you expand the given like this: $a (b-c) = ab \boxed{+} ac = 32$ , you will obtain $ab = 32 - ac = 32 - 8 = 24$ .

(D)
Tip:Just because a number appears in the question doesn't mean it is the answer.
If $ab = 32$ , then $a(b-c) = ab - ac = 32 - 8 = 24$ , which is not equal to 32.