Question

Keith sold half of his comic books and then bought 9 more. He now has 15. How many did he begin with?

Answer 1

Hint: Here we will assume that Keith has started with x books. Then according to given information or data we will form an equation using the variable x. That will be an equation with one variable. And then solving the equation will give the value of x that is the number of books he initially had.

Complete step by step solution:
Let Keith have x books when he started.
According to the question he then sold half of his books.
So the equation will be,
 \[x - \dfrac{x}{2} = \dfrac{x}{2}\]
Now after selling his books, he added some more books to his collection. That is he bought 9 more books. And now he has 15 books with him.
So the equation will change to,
 \[\dfrac{x}{2} + 9 = 15\]
So we will solve this equation now.
First take the constant numbers on one side,
 \[\dfrac{x}{2} = 15 - 9\]
 \[\dfrac{x}{2} = 6\]
Now on cross multiplying we get,
 \[
  x = 6 \times 2 \\
  x = 12 \;
\]
This is the number of books he initially had.
So, the correct answer is “ x = 12”.

Note: Here we can note the way the data is to be used. Question is very simple to be solved. Also note that there is no need to judge the number of books he initially had. Like using trial and error methods. This equation forming and solving will give the exact answer. Note that the number of unknowns is equal to the number of equations so formed.