So gonna do opposites
6+6=12
12= 3/4th of the entire box
4=1/4th of the entire box
12+4=16
There was 16 chocolates originally.
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
[tex]n_w=\dfrac{1}{4}c=\dfrac{c}{4}.[/tex]
Now, at the dinner, number of candies ate by Byron and his friends is
[tex]n_d=\dfrac{1}{2}\times\left(c-\dfrac{c}{4}\right)=\dfrac{1}{2}\times\dfrac{3c}{4}=\dfrac{3c}{8}.[/tex]
Since only 6 candies left in the box, so we have
[tex]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.[/tex]
Thus, the number of candies that the box contain to start with is 16.
