SOLUTION: 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

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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. ThanksThis question is from textbook

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

332%2Aabs%28x-11%29%2B17000=18700 Start with the given equation


332%2Aabs%28x-11%29=1700 Subtract 17,000 from both sides.


abs%28x-11%29=5.12048 Divide both sides by 332 (this is an approximate value)



Break up the absolute value (remember, if you have abs%28x%29=a, then x=-a or x=a)

x-11=-5.12048 or x-11=5.12048 Set the expression x-11 equal to the original value 5.12048 and it's opposite -5.12048




Now lets focus on the first equation x-11=-5.12048


x=-5.12048%2B11Add 11 to both sides


x=5.87952 Combine like terms on the right side


So rounding to the nearest whole number, we get x=6


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 x-11=5.12048



x=5.12048%2B11Add 11 to both sides


x=16.12048 Combine like terms on the right side


So rounding to the nearest whole number, we get x=16



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.



=========================================


Answer:

So we got the solutions (after rounding to the nearest whole number) x=6 and x=16. 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(48547) About Me  (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,
------------------------------------------------------
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
=======================
Cheers,
Stan H.