SAT Change the Subject

Algebra Level 1

If $a = 3b - 2c$ , which of the following is an expression for $b$ ?

(A) $\ \ 3b - 2c$

(B) $\ \ a + 2c$

(D) $\ \ \frac{a+2c}{3}$

(E) $\ \frac{3b-a}{2}$

A B C D E

1 solution

Tatiana Georgieva Staff
Feb 1, 2015

Correct Answer: D

Solution:

Tip: Follow order of operations.

$\begin{array} { l l l l } 3b - 2c & = a & \text{given} & (1) \\ 3b & = a + 2c & \text{add 2c to both sides} & (2)\\ b & = \frac{a+2c} {3} & \text{divide by 3 on both sides} & (3) \\ \end{array}$

Incorrect Choices:

(A)
Tip: Just because a number appears in the question doesn’t mean it is the answer.
This is just the expression for $a$ .

(B)
Tip: Read the entire question carefully.
If you stop at step $(2),$ you will obtain $a + 2c$ . However, this equals $3b$ , not $b$ .

(C)
Tip: Read the entire question carefully.
If you swap the coefficients of $b$ and $c$ like this, $a = \boxed{2}b - \boxed{3} c$ , then solving for $b$ will give $b = \frac{ a + 3c } { 2 } .$

(E)
Tip: Read the entire question carefully.
If you solve for $c$ , you will obtain this wrong answer.

SAT Change the Subject

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