5 buckets contain a total of 100 tennis balls. How many balls are in each bucket if each bucket contains n more balls than the previous bucket? Find all the possible values for n.
f is number in 1st bucket
5 f + 10 n = 100
f + 2 n = 20
To find the number of balls in each bucket, we need to find the value of n. Let's go step by step to solve the problem:
Step 1: Let's assume the number of balls in the first bucket is x.
Step 2: The second bucket will contain x + n balls because it has n more balls than the first bucket.
Step 3: The third bucket will contain x + 2n balls because it has 2*n more balls than the first bucket.
Step 4: The fourth bucket will contain x + 3n balls because it has 3*n more balls than the first bucket.
Step 5: The fifth bucket will contain x + 4n balls because it has 4*n more balls than the first bucket.
Now, the sum of the number of balls in all the buckets is 100. So, let's write the equation:
x + (x + n) + (x + 2n) + (x + 3n) + (x + 4n) = 100
Simplifying this equation, we get:
5x + 10n = 100
Divide both sides of the equation by 5:
x + 2n = 20
Now, we can see that there are infinitely many possibilities for the values of n that satisfy this equation. Let's find a general expression for n in terms of x:
n = (20 - x) / 2
Therefore, all possible values of n can be represented as (20 - x) / 2, where x can be any value.
For example:
- If x = 10, then n = (20 - 10) / 2 = 5
- If x = 5, then n = (20 - 5) / 2 = 7.5 (which is not a whole number)
So, the possible values for n are all the even numbers greater than or equal to 0.