Question

Mike sold one-third of his novels. He gave 2 novels to his friend Tom. He is left with 8 novels.
Derive an algebraic expression from the above comprehension to find the number of novels he had initially.

• A. $2=\frac{2x}{3}-8$
• B. $8=\frac{2x}{3}+2$
• C. $8=\frac{x}{3}-2$
• D. $8=\frac{2x}{3}-2$

Answer 1

The correct option is D $8=\frac{2x}{3}-2$

Let the number of novels Mike had intially be $x$

Given,
Number of novels sold $=\frac{1}{3}\times x$
Remaining number of novels after sale $=(1-\frac{1}{3})\times x=\frac{2x}{3}$

The number of novels given to Tom = 2
Finally, the number of novels left = 8

Finally, number of novels left = Remaining number of novels after sale - Number of novels given to Tom
$\Rightarrow 8=\frac{2x}{3}-2$