abbycross167
  • abbycross167
Will someone please help me figure out how to answer this question? At Generic High School, in the year 2001, there were 20 students per every computer. In 2008, there were 4.5 students per computer. During which year were there 10 students per computer?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
is this relation supposed to be linear?
anonymous
  • anonymous
if so, in 8 years it went from 20 to 4.5 making your slope \(\frac{4.5-20}{8}\)
abbycross167
  • abbycross167
Umm I really don't know... I think so

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abbycross167
  • abbycross167
@satellite73
anonymous
  • anonymous
\[\frac{4.5-20}{7}=-\frac{31}{14}\]
anonymous
  • anonymous
your linear model is \[y=-\frac{31}{14}+20\] set that equal to \(10\) and solve for \(x\)
anonymous
  • anonymous
that is wrong sorry it is\[y=-\frac{31}{14}x+20\]
abbycross167
  • abbycross167
17 11/14?
abbycross167
  • abbycross167
@jim_thompson5910 could you please try to help me answer the question?
jim_thompson5910
  • jim_thompson5910
ok one moment
abbycross167
  • abbycross167
ok thank you
jim_thompson5910
  • jim_thompson5910
use the equation @satellite73 wrote out plug in y = 10 and solve for x \[\Large y = -\frac{31}{14}x + 20\] \[\Large 10 = -\frac{31}{14}x + 20\] \[\Large 10-20 = -\frac{31}{14}x + 20-20\] \[\Large -10 = -\frac{31}{14}x\] do you see how to finish?
abbycross167
  • abbycross167
umm maybe... would I divide -31/14 by -10?
jim_thompson5910
  • jim_thompson5910
or multiply both sides by the reciprocal of the fraction
abbycross167
  • abbycross167
ok would you mind showing me so I know i got it right?
jim_thompson5910
  • jim_thompson5910
ok so we have this equation |dw:1449637397806:dw|
jim_thompson5910
  • jim_thompson5910
multiply both sides by -14/31 this is the reciprocal of -31/14 |dw:1449637448465:dw|
jim_thompson5910
  • jim_thompson5910
notice these cancellations |dw:1449637499124:dw|
abbycross167
  • abbycross167
okay so now what? -10* -14/31= 4 16/31?
jim_thompson5910
  • jim_thompson5910
which is approximately 4.516129032
jim_thompson5910
  • jim_thompson5910
so when the value of x is approx 4.516129032, the value of y will be 10 it means that the point in time when there are 10 students per computer is roughly 4.516129032 years after 2001 so between the years 2005 and 2006
abbycross167
  • abbycross167
okay wow... you made this look sooo easy! I can't thank you enough!!!
jim_thompson5910
  • jim_thompson5910
no problem

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