Question 1105031
The collie's weight is a straight line over the 4 wks
You are given 2 points on that line
The St. Bernard's weight is a straight line over the 4 wks
You are given 2 points on that line
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Call the start of the 4 wk period {{{ t = 0 }}}
Let {{{ m }}} = mass in kg
The 2 points for the collie:
( 0, 13.4 ) 
( 4, 17 )
The 2 points for the St. Bernard:
( 0, 6 )
( 4, 12.4 )
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Use the general point-slope formula:
For collie:
{{{ ( m - 13.4 ) / ( t - 0 ) = ( 17 - 13.4 ) / ( 4 - 0 ) }}}
{{{ ( m - 13.4 ) / t = 3.6 / 4 }}}
{{{ ( m - 13.4 ) / t = .9 }}}
{{{ m - 13.4 = .9t }}}
{{{ m = .9t + 13.4 }}}
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For St. Bernard:
{{{ ( m - 6 ) / ( t - 0 ) = ( 12.4 - 6 ) / ( 4 - 0 ) }}}
{{{ ( m - 6 ) / t = 6.4 / 4 }}}
{{{ ( m - 6 ) / t = 1.6 }}}
{{{ m - 6 = 1.6t }}}
{{{ m = 1.6t + 6 }}}
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find the intersection of the lines:
Set the masses equal to eachother
{{{ .9t + 13.4 = 1.6t + 6 }}}
{{{ .7t = 7.4 }}}
{{{ t = 10.57 }}}
and
{{{ m = 1.6t + 6 }}}
{{{ m = 1.6*10.57 + 6 }}}
{{{ m = 16.91 + 6 }}}
{{{ m = 22.91 }}} kg
Their masses will both be 22.91 kg in 10.57 weeks
Check the math