Question 390844: I am trying to help my daughter understand how to solve a word problem but can't remember how to solve it myself -
"If sales of 30 cattle bring in a profit of $4500 and sales of 50 cattle bring in a profit of $12,500, and the profit model is linear, how much profit will the sale of 75 cattle bring in?"
$4,500 divided by 30 = $150 per head
$12,500 divided by 50 = $250 per head
my thought was that linear would mean 75 x $350 = $26,250 but that was not one of the multiple choice answers
Found 3 solutions by stanbon, scott8148, solver91311:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If sales of 30 cattle bring in a profit of $4500 and sales of 50 cattle bring in a profit of $12,500, and the profit model is linear, how much profit will the sale of 75 cattle bring in?
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You have two points relating # of cattle and profit:
(30,4500) and (50,12500)
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The linear equation has the form p = mc + b
where p is profit and c is number of cattle.
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m is the slope of the equation:
m = (12500-4500)/(50-30) = 8000/20 = 400
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Find "b" using p=4500 when c=30 and m = 400:
4500 = 400*30 + b
b = 4500-12000
b = -7500
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Equation:
p(c) = 400c - 7500
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Solve: "how much profit will the sale of 75 cattle bring in?"
p(75) = 400*75 - 7500
p(75) = $22,500
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Cheers,
Stan H.
Answer by scott8148(6628)  (Show Source):
You can put this solution on YOUR website! the linear profit model means that the income per steer (slope) is constant , but there is also overhead or fixed costs (intercept)
20 more cattle (50 - 30) bring in 8000 more dollars (12500 - 4500)
so the income per steer is ___ 8000/20 or 400
30 cattle means income of 12000 , but only 4500 profit
this indicates a fixed cost (overhead) of 7500 ___ this checks out for 50 cattle
the equation is ___ p = 400c - 7500
plug in 75 for c to find your answer
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
This is nothing more than creating an equation given two ordered pairs and then using the equation to predict the location of a third point. Instead of the normal x-y coordinate plane, you have a set of axes labeled 'Profit' on the vertical and 'Cattle sold' on the horizontal. A point on your plane would then be identified by an ordered pair (c, p) where c is the number of cattle sold and p is the corresponding profit.
You are given two points, namely (30,4500) and (50,12500)
To derive your equation, use the two-point form of an equation of a straight line, namely:
(x\ -\ x_1) )
where ) and ) are the coordinates of the given points.
Just fill in the numbers and do the necessary arithmetic to simplify your equation. Once you have the equation written, substitute 75 for x and calculate the value of y, that is the profit that corresponds. Let me know what you get for an answer.
John
My calculator said it, I believe it, that settles it
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