Answer: I got you!
Explanation:
(a) To find the number of bottles of sanitizer received by each person, we need to divide the total number of bottles by the number of people. So:
Number of bottles per person = (p² + 29p - 96) ÷ (p + 32)
(b) If we substitute x = 8 into the expression for the number of bottles of sanitizer, we get:
p² + 29p - 96 = x(x + 32)
p² + 29p - 96 = 8(8 + 32)
p² + 29p - 96 = 320
p² + 29p - 416 = 0
We can solve this quadratic equation to get:
p = -32 or p = 13
Since the number of people cannot be negative, we take p = 13. Therefore, the actual number of bottles of sanitizer distributed is:
p² + 29p - 96 = 13² + 29(13) - 96 = 520
The number of people who received the sanitizer is:
p + 32 = 13 + 32 = 45
And the share of each person is:
Number of bottles per person = (p² + 29p - 96) ÷ (p + 32) = 520 ÷ 45 ≈ 11.56
So each person received approximately 11.56 bottles of sanitizer.