What is the mistake in this approach to find the average

Question

The captain of a Football team of 11 members is 26 years old and the GoalKeeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

Answer : 23 years.

my (wrong) solution :

Let the total Age of the Team be "x" . ---> equation (1)

Average of the team = x / 11 

According to the question : 

The average age of the team (Excluding Captain and GoalKeeper)

Total age of the team - (captain's age - GoalKeeper's age) / 9 . 

Captain age = 26 , Goal Keeper age = 29 . Total age to be removed = 55

x - 55 / 9

Given in the question is that this average is one year less than the
the average of the whole team .

[x-55/9] - 1 = x / 11 

solving this equation . x = 352 .

according to equation(1) 352 / 11 = 32 (average age of the team)

This however is the wrong answer . Where have i gone wrong ?

Answer 1

Plus 1 instead of minus 1. $$\frac{x-55}9+1=\frac x{11}.$$ Leads to $x=253$.

Answer 2

When you compute the average age of the team without the captain and goalkeeper it should be (total age of team-captain's age-goalkeeper's age)/9. You put the opening parenthesis before the captain's age so the total age of the team would not be divided by $9$. You also subtracted the $1$ year from the wrong side as we are told that removing them lowers the age. You then would get $$\frac {x-55}9=\frac x{11}-1\\ \frac {2x}{99}=\frac {46}9\\ x=253$$ and the average age is $$\frac {253}{11}=23$$

Answer 3

Let $N$ be the sum of the ages of the other players.

So the total sum of all the players' ages is $N + 55$

We know that

$N/9 = (N+55) / 11 + 1$

Which gives

$N = 198$

So the total age of the players is $198 + 55 = 253$

So the average age of all the players is

$253 / 11 = 23$

Answer 4

Firstly, the age of captain is 26 and goal keeper is 29. let x be the average of the team including captain and goal keeper. Let y be the average of team excluding captain and goalkeeper.

y=x-1

Compute x (Average of team including captain and goalkeeper) = (Sum of ages of nine players+age of captain + age of goal keeper)/11

Computer y (Average of team including captain and goalkeeper) = (Sum of ages of nine players)/9

As y=x-1

(Sum of ages of nine players)/9 = (Sum of ages of nine players+age of captain + age of goal keeper)/11 )-1

Solve this equation:

(Sum of ages of nine players)/9 =(Sum of ages of nine players+age of captain + age of goal keeper -11)/11.

Use cross multiplication technique

11(Sum of ages of nine players)= 9(Sum of ages of nine players)+9(age of captain)+9(age of goalkeeper)-99

2(Sum of ages of nine players) = 9(age of captain)+9(age of goalkeeper)-99

2(Sum of ages of nine players) = 9(26)+9(29)-99

2(Sum of ages of nine players) = 234+261-99

2(Sum of ages of nine players) = 495-99

2(Sum of ages of nine players) = 396

Sum of ages of nine players = 396/2 =198

Now compute x

x = (Sum of ages of nine players+age of captain + age of goal keeper)/11

x = (198+26+29)/11

x = 253/11

x= 23

to check whether your answer is correct computer y and check whether y =x-1.