Question

Given:
Expression 1: $\frac{4}{3}$x + 29
Expression 2: 12x + 261

Which one of the following statements represents the correct relation between both the expressions?

• A. Expression 2 is 6 times that of Expression 1.
• B. Expression 2 is 9 times that of Expression 1.
• C. Expression 2 is 12 times that of Expression 1.
• D. Expression 2 is 15 times that of Expression 1.

Answer 1

The correct option is B Expression 2 is 9 times that of Expression 1.

Given:
Expression 1: $\frac{4}{3}$x + 29
Expression 2: 12x + 261


Now,
12 can be factored as 9 $\times$ $\frac{4}{3}$

Similarly,
261 can be factored as 9 × 29.

Writing 12x + 261 in terms of factors,
$\Rightarrow$ 12x + 261 = ($\frac{4}{3}$ × 9)x + (29 × 9)
= 9 × ($\frac{4}{3}$x + 29)

Hence,
Expression 2 = 9 × Expression 1