SOLUTION: A student is asked his age and he responds "my age is nine less than half my professor's age". The professor is asked her age and she responds "my age is three times my student's a

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Question 307665: A student is asked his age and he responds "my age is nine less than half my professor's age". The professor is asked her age and she responds "my age is three times my student's age". What is the age of the student?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A student is asked his age and he responds "my age is nine less than half my professor's age".
The professor is asked her age and she responds "my age is three times my student's age".
What is the age of the student?
:
let s = student's age
let p = prof's age
:
Write an equation for each statement:
:
"my age is nine less than half my professor's age".
s = .5p - 9
:
"my age is three times my student's age".
p = 3s
:
replace p with 3s in the 1st equation:
s = .5(3s) - 9
s = 1.5s - 9
9 = 1.5s - 1s
9 = .5s
mult both sides by 2
s = 18 yrs is student's age
:
:
Check solution in the 1st statement;
p = 3(18)
p = 54 prof's age
"my age is nine less than half my professor's age".
18 = .5(54) - 9
18 = 27 - 9