Question

Which one of the following statements represents the correct relation between the given expressions?
Expression 1 : $\frac{13}{2}$x + 65
Expression 2 : 26x + 260

• A. Expression 2 is 2 times that of Expression 1.
• B. Expression 2 is 3 times that of Expression 1.
• C. Expression 2 is 4 times that of Expression 1.
• D. Expression 2 is 6 times that of Expression 1.

Answer 1

The correct option is C Expression 2 is 4 times that of Expression 1.

Expression 1: $\frac{13}{2}$x + 65
Expression 2: 26x + 260


Now,
26x can be factored as 4 $\times$ $\frac{13}{2}$x

Similarly,
260 can be factored as 4 $\times$ 65

Writing 26x + 260 in terms of factors,

($\frac{13}{2}x$ × 4) + (65 × 4)

= 4 × ($\frac{13}{2}x$+ 65)

$\therefore$ Expression 2 = 4 × Expression 1