SOLUTION: Amy is one year older than Ben the sum of their ages is greater than 33 and less than 45 find all possible ages of Ben

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Question 1184508: Amy is one year older than Ben the sum of their ages is greater than 33 and less than 45 find all possible ages of Ben
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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Amy is one year older than Ben. The sum of their ages is greater than 33 and less than 45. Find all possible ages of Ben.
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33%3Cb%2B1%2Bb%3C45

33%3C2b%2B1%3C45
32%3C2b%3C44
highlight%2816%3Cb%3C22%29

Answer by ikleyn(52799) About Me  (Show Source):
You can put this solution on YOUR website!
.
Amy is one year older than Ben the sum of their ages is greater than 33 and less than 45 find all possible ages of Ben
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Let "b" be the Ben's age.

Then Amy's age is (b+1) years.


From the condition, we have this compound inequality


    33 < b + (b+1) < 45


Simplify and solve for b


    33 < 2b + 1 < 45.


Subtract 1 from all three terms


    32 < 2b < 44.


Divide by 2 all the terms 


    16 < b < 22.


It is the ANSWER  to the problem's question.

Solved.