After eating half of the chocolate mini bars in a can, Clayton gave one fourth of the remaining mini bar chocolates to his buddy and realized that he only had 6 chocolate mini bars left. How many mini bar chocolates did he originally have?
(A) 2
(B) 4
(C) 8
(D) 16
(E) 18
OA is D
pls, I need an Expert to give me a perfect interpretation of this question.Thanks
Hi Roland2rule,
Let's take a look at your question.
Let 'x' be the total chocolates in the can.
After eating half of the chocolate mini bars in a can, remaining chocolates will be:
$$x-\frac{1}{2}x=\frac{1}{2}x$$
Clayton gave one fourth of the remaining mini bar chocolates to his buddy.
$$=\left(\frac{1}{4}\right)\frac{1}{2}x=\frac{1}{8}x$$
After giving chocolates to his buddy, only 6 chocolate mini bars left. We can write it as:
$$\frac{1}{2}x-\frac{1}{8}x=6$$
$$x\left(\frac{1}{2}-\frac{1}{8}\right)=6$$
$$x\left(\frac{4-1}{8}\right)=6$$
$$x\left(\frac{3}{8}\right)=6$$
$$x=6\times\frac{8}{3}$$
$$x=2\times8=16$$
Hence, there were 16 chocolates in the can originally.
Therefore, Option
D is correct.
Hope it helps.
I am available if you'd like any follow up.
