If the product of two numbers is 96 and the sum is 35, the greatest number would be ______?
Answer: 32
Explanation
Let's denote the two numbers as x and y.
Given:
xy = 96 ... (1)
x + y = 35 ... (2)
We can rewrite equation (2) as:
y = 35 - x
Substitute this into equation (1):
x(35 - x) = 96
35x - x² = 96
x² - 35x + 96 = 0
Factoring the quadratic equation:
(x - 3)(x - 32) = 0
x = 3 or x = 32
If x = 3, y = 32
If x = 32, y = 3
The greatest number is 32.
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