Word problem teaser.?

The fixed costs to produce a sport shoe are $4000. If 200 pairs cost a total of $5050, find a linear equation giving the total cost, c, in terms of x, the number of pairs of shoes produced.

Word problem teaser.?
The problem statement gives two ordered pairs (x, c). They are (0, 4000) and (200, 5050). Pick your favorite formula for the equation of a line. Mine happens to be the slope intercept formula:


c(x) = m*x + b, where c(x) = cost as a function of number of shoes, m = slope, x = number of shoes, b = c(x)-intercept.





One of the ordered pairs happens to be the c(x)-intercept. When x = 0, c(x) = 4000.





All we need to do is calculate the slope of the line:


slope = (c(x2) - c(x1))/(x2 - x1) = (5050-4000)/(200 - 0)


slope = 1050/200 = 5.25





Now let's plut the slope and intercept back into the equation for a line:


c(x) = m*x + b


c(x) = 5.25*x + 4000





The units of the slope are $/shoe. the units for the intercept are $.
Reply:c = mx + b.





From what we're given, 5050 = 200m + 4000.





So, 200m = 1050, m = 5.25





Thus, c(x) = 5.25x + 4000



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