Gorilla Studies

Divide 330/11 and get the average number of bananas given to each of the gorillas.The middle gorilla #6 will receive exactly the same number as the average i.e. 30 thus on counting further ( incrementing by one) we see that #11 receives 35

There are $11$ gorillas in the clan, Gorilla $_5$ and the $10$ others. The total number of bananas received will equal $x+(x+1)+(x+2)+\ldots+(x+10).$ Gorilla $_1$ will get $x$ bananas, so Gorilla Supreme will get $x+10$ bananas. This is just $11x$ plus the sum of the first $10$ integers, so it is equal to this. $11x+\dfrac{10\times11}{2}=11x+55=330$ Solving for $x$ gives $x=25\text{,}$ so Gorilla $_1$ will get $25$ bananas. Therefore, Gorilla Supreme will get $25+10=\boxed{35}$ bananas.

Total Number of Gorillas - 1 + 10 Total Bananas = 330 Formula for n =11, 11x + (Sum of (1 to 10)) = 11x + 55 Now, since the total bananas are 330 equating it to the above equation we get, 11x + 55 = 330 or x = 25. Now the supreme Gorilla is the 11th Gorilla which gets x + 10 bananas or 25+10 = 35 bananas. Hence the answer is 35 bananas

It's an AP with constant difference (d)=1 So,S=(n/2)x[2X+(n-1)d] gives X=25 So,11th term is 25+20(1)=35

There are a total of 11 gorillas and the division of bananas will be like this: x + x+1 + x+2..........x+10=330.On solving x=25.

Due to the rank difference the Supreme Gorilla gets x+10=35 bananas

Total number of Gorillas: 11

Total Bananas: 330

Number of bananas each gorilla gets increases in Arithmetic Progression.

Therefore total bananas = 11 x + (1+2+3..+10)

                    then,  330  = 11*x*  + (10)(10+1)/2

solving further 330 = 11 x + 55

            we get       *x* = 25

Supreme Gorilla gets: x + 10 = 35 bananas

So let's determine how many gorillas are in the clan. You can see from the problem that there are 11 gorillas in the clan, not 10. It states that he has to get himself and 10 others bananas.

Now let's solve.

Let x = the number of bananas.

If there are $n$ gorillas, then the equation would be $(n \times x) + (1-1) + (2-1) + (3-1) ... + (n-1) = \text{Number of bananas}$ If there are $11$ gorillas, then the equation would be $(11x) + (1-1) + (2-1) + (3-1) ... + (11-1) = \text{Number of bananas}$ Can you see why? Look at the above problem; it states that each gorilla gets a definite number of bananas and additional bananas based on their rank, which is n-1, n stands for rank number.

If we complete the formula, we see this:

$11x + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 330$ $11x + 55 = 330$ $11x = 275$ $x = 25$

Yay! We got 25! Is that our answer? NO. The Supreme Gorilla is not happy when you underestimate him. $x$ is for the definite number of bananas that everyone is guaranteed getting. The supreme gorilla deserves (11-1), 10 extra bananas, since he is $Gorilla_{11}$ . Now we can get our definite answer.

$25 \text{ from the definite number of bananas } + 10 \text{ from the extra number of bananas } = \boxed{35 \text{bananas}}$