Question

Byron purchased a box of candy at the store. On his way home he ate ¼ of the candy in the
box. At dinner with friends later that night he served ½ of what was left. If there are 6
chocolates now left in the box, how many did the box contain to start with?

Answer 1

Answer: The number of candies that the box contain to start with is 16.

Step-by-step explanation: Given that Byron purchased a box of candy at the store. On his way home he ate one-fourth of the candy in the box and at dinner with friends later that night he served half of what was left.

We are to find the number of candies that the box contain to start with if there are only 6 candies left in the box.

Let c represents the number of candies in the box to start with.

So, on his way home, number of candies ate by Byron is given by

$n_w=\dfrac{1}{4}c=\dfrac{c}{4}.$

Now, at the dinner, number of candies ate by Byron and his friends is

$n_d=\dfrac{1}{2}\times\left(c-\dfrac{c}{4}\right)=\dfrac{1}{2}\times\dfrac{3c}{4}=\dfrac{3c}{8}.$

Since only 6 candies left in the box, so we have

$\begin{gathered}c-n_w-n_d=6\\\\\Rightarrow c-\dfrac{c}{4}-\dfrac{3c}{8}=6\\\\\\\Rightarrow \dfrac{8c-2c-3c}{8}=6\\\\\\\Rightarrow \dfrac{3c}{8}=6\\\\\\\Rightarrow c=\dfrac{6\times8}{3}\\\\\Rightarrow c=16.\end{gathered}$

Thus, the number of candies that the box contain to start with is 16.