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?
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.