Question 174669
Let the flat rate for the 1st 8 min = {{{k}}}
Let the cost/min after the 8 min = {{{c}}}
Let {{{t}}}= the time in minutes after 8 min that it takes to wash car
Let {{{C}}} = the toal cost to wash car
{{{C = ct + k}}}
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For Gina:
{{{8 + t[g] = 12}}}
{{{t[g] = 4}}}
{{{C[g] = 5}}}
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For Kris:
{{{8 + t[k] = 17}}}
{{{t[k] = 9}}}
{{{C[k] = 6.25}}}
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Now put the data from each case into the geral equation:
(1){{{5 = 4c + k}}}
(2){{{6.25 = 9c + k}}}
There are 2 equations and 2 unknowns, so it's solvable
Subtract (1) from (2)
{{{1.25 = 5c}}}
{{{c = .25}}}
Now find {{{k}}}
(1){{{5 = 4c + k}}}
{{{5 = 4*.25 + k}}}
{{{k = 5 - 1}}}
{{{k = 4}}}
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Now I can rewrite the general equation as:
{{{C = .25t + 4}}}
Here's a plot:
{{{ graph( 500, 500, -5, 15, -5, 15,(1/4)*x + 4 ) }}}
The slope is {{{1/4}}}