Question

The pirates won exactly 4 of their 15 games. They then played N remaining games and won all of them. If they won exactly half of all the games they played, what is the value of N?

Answer 1

Hint: Find the number of games won by the pirate by using both the given conditions before and after N games were played, and we will get two expressions after this step, then we equate them both to find the value of N.

Complete step-by-step solution:
Let us consider the condition given in the question that the pirates won exactly 4 of their 15 games. Also, when the pirates played N extra games they won all of them. This means that the total number of games that the pirate won are 4 from before playing N games and N after playing N games.
$ \Rightarrow {\text{Total games won}} = 4 + N$

The objective is to find the value of N if the pirates won exactly half of all the games played.

For this we first find the total number of games played. As it is given that the pirates won 4 out of 15 games played, thus before playing N extra games, the number of games played were 15. Thus, after playing N more games, the total becomes N+15.

Now, we are given that half of the total games played were a winning game for them.
$ \Rightarrow {\text{Total games won}} = \dfrac{{N + 15}}{2}$

Now we equate the expression for total games won in both the cases to find the value of N.
$
   \Rightarrow 4 + N = \dfrac{{N + 15}}{2} \\
   \Rightarrow 8 + 2N = N + 15 \\
   \Rightarrow N = 7 \\
$

Hence, if they won exactly half of all the games they played, the value of N is 7.

Note: In the condition-based questions, list down the mathematical translation of the given conditions and try to establish a relation between each of them to find the value of the missing variable. Be careful to consider each condition and not to skip any thinking it is irrelevant. Each condition will have its own significance.