Brandon had 40% more balls than Cody. Brandon gave 30% of his balls to Cody. Cody in return gave 50% of his balls to Brandon. Within the conclusion, Cody had 852 less balls than Brandon. How numerous balls did Brandon have at to begin with?

Answer 1

Let's start by using variables to represent the number of balls Brandon and Cody had at the beginning:

- Let B be the number of balls Brandon had at the beginning.
- Let C be the number of balls Cody had at the beginning.

From the problem statement, we know that Brandon had 40% more balls than Cody:

B = (1 + 0.4)C
B = 1.4C

We also know that Brandon gave 30% of his balls to Cody:

B' = 0.7B
C' = C + 0.3B

And Cody in return gave 50% of his balls to Brandon:

C'' = 0.5C'
B'' = B' + 0.5C'

We want to find B'' - C''. We can simplify this expression by substituting B' and C':

B'' - C'' = (B' + 0.5C') - (C'')
= (0.7B + 0.5C) - 0.5(C + 0.3B)
= 0.2B + 0.2C

Now we can use the fact that Cody had 852 less balls than Brandon:

B - C = 852
1.4C - C = 852
0.4C = 852
C = 2130

Finally, we can substitute C into the expression we found for B'' - C'':

B'' - C'' = 0.2B + 0.2C
= 0.2B + 0.2(2130)
= 0.2B + 426

We know that B'' - C'' = 852, so we can set up an equation:

0.2B + 426 = 852
0.2B = 426
B = 2130

Therefore, Brandon had 2130 balls at the beginning.