Question 167751This question is from textbook
: I am working on equations with absolute value and I need help with this word problem, please.
The problem reads:
The number of U.S. teenagers in the age category "15-19-years olds" during any year between 1980 and 1998 can be modeled approximately by
T=332/x-11.5/+17000
where T is the number of "15-19-years-olds" in thousands and x is the number of years since January 1, 1980 (U.S. Census Bureau, Current Poplulatioin Reports.) Use the model to determine the year in which the number of 15-19-year olds in the U.S. was 18,700,000 (18,700 thousands).
The book comes up with the answer of 1986 and 1996, I cant even come close to them years....please help. Thanks
This question is from textbook
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
 Start with the given equation
 Subtract 17,000 from both sides.
 Divide both sides by 332 (this is an approximate value)
Break up the absolute value (remember, if you have  , then  or  )
 or  Set the expression  equal to the original value 5.12048 and it's opposite -5.12048
Now lets focus on the first equation
 Add 11 to both sides
 Combine like terms on the right side
So rounding to the nearest whole number, we get 
This means that 6 years from the beginning (which is 1980), the population of 15-19 yr olds was 18,700,000.
So in 1986 (which is 6 years away from 1980), the population of 15-19 yr olds was 18,700,000.
Now lets focus on the second equation
 Add 11 to both sides
 Combine like terms on the right side
So rounding to the nearest whole number, we get 
This means that 16 years from the beginning (which is 1980), the population of 15-19 yr olds was 18,700,000.
So in 1996 (which is 16 years away from 1980), the population of 15-19 yr olds was 18,700,000.
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Answer:
So we got the solutions (after rounding to the nearest whole number) and . These solutions represented the number of years after 1980.
So in 1986 and in 1996 the population of 15-19 year olds was 18,700,000
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The number of U.S. teenagers in the age category "15-19-years olds" during any year between 1980 and 1998 can be modeled approximately by
T=332*|x-11.5| + 17000
where T is the number of "15-19-years-olds" in thousands and x is the number of years since January 1, 1980 (U.S. Census Bureau, Current Poplulatioin Reports.) Use the model to determine the year in which the number of 15-19-year olds in the U.S. was 18,700,000 (18,700 thousands).
The book comes up with the answer of 1986 and 1996,
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18,700 = 332*|x-11.5| + 17000
-----
332*|x-11.5| = 1700
|x-11.5| = 5.12..
x-11.5 = 5.12 or x-11.5 = -5.12...
x = 16.62 or x = 6.38
--------------------------
1980 + 6.38 = 1986
1980 + 16.62 = 1996
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Cheers,
Stan H.
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