SOLUTION: The sum of two numbers is 30. Find what values of two numbers that would make their product be greater than 125

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Question 1038692: The sum of two numbers is 30. Find what values of two numbers that would make their product be greater than 125
Answer by Fombitz(32388) About Me  (Show Source):
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A%2BB=30
A=30-B
.
.
.
AB%3E125
Substituting,
%2830-B%29B%3E125
30B-B%5E2%3E125
B%5E2-30B%2B125%3C0
%28B-25%29%28B-5%29%3C0
Break up the number line into 3 regions,
B%3C5
5%3CB%3C25
B%3E25
Test the inequality in each region to see which satisfies the inequality.
B%3C5
B=4%7D%7D%0D%0A%7B%7B%7B%284-25%29%284-5%29%3C0
-21%28-1%29%3C0
21%3C0
False.
5%3CB%3C25
B=6%7D%7D%0D%0A%7B%7B%7B%286-25%29%286-5%29%3C0
-19%281%29%3C0
-19%3C0
True.
B%3E25
B=26%7D%7D%0D%0A%7B%7B%7B%2826-25%29%2826-5%29%3C0
1%2821%29%3C0
21%3C0
False.
So then,
5%3CB%3C25
which then leads to
5%3C30-A%3C25
-25%3C-A%3C-5
25%3CA%3C5
or
5%3CA%3C25