Question 1062666
There is an inverse linear relation ( I assume ) between
price of bottles and number of bottles sold
You are given 2 points on the line:
( 200, .8 ) and
( 150, 1 )
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Let {{{ n }}} = number of bottles sold
Let {{{ p }}} = price/bottle for {{{ n }}} bottles sold
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Use the point-slope formula
{{{ ( p - .8 ) / ( n - 200 ) = ( 1 - .8 ) / ( 150 - 200 ) }}}
{{{ ( p - .8 ) / ( n - 200 ) = .2 / (-50 ) }}}
Multiply both sides by {{{ ( n - 200 )*( -50 ) }}}
{{{ ( -50 )*( p - .8 ) = .2*( n - 200 ) }}}
{{{ -50p + 40 = .2n - 40 }}}
{{{ -50p = .2n - 80 }}}
Multiply both sides by {{{ -1 }}}
{{{ 50p = -.2n + 80 }}}
{{{ p = - .004n + 1.6 }}}
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If {{{ p = .9 }}}
{{{ .9 = -.004n + 1.6 }}}
{{{ .004n = .7 }}}
{{{ n = 175 }}}
175 bottles will be sold at $.90/bottle
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check:
Does the equation go through ( 200, .8 ) ?
{{{ p = - .004n + 1.6 }}}
{{{ .8 = - .004*200 + 1.6 }}}
{{{ .8 = -.8 + 1.6 }}}
{{{ .8 = .8 }}}
OK
Does the equation go through ( 150,1 ) ?
{{{ p = - .004n + 1.6 }}}
{{{ 1 = - .004*150 + 1.6 }}}
{{{ 1 = - .6 + 1.6 }}}
{{{ 1 = 1 }}}
OK