Question

A hot-dog stand owner makes a profit of $100 when he sells 90 hot dogs a day. He has a loss of $30 when he sells 25
hot dogs a day. Write a linear equation that represents his profit?


No idea what I am supposed to do.
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100=90d
-30=25d

Answer 1

let x = number of hotdogs sold

let s = sell price of hotdog

let c = fixed operating costs

p = profit

p = x s - c

substitute to find s and c

100 = 90 s - c

-30 = 25 s - c

adding equations ... 130 = 65 s ... 2 = s

100 = 90 * 2 - c ... 80 = c

p = 2 x - 80

Answer 2

you have two ordered pairs of the type (h, p)
namely (90,100) and (25, -30)
slope = (-30-100)/(25-90) = 2

p-100 = 2(h-90)
p = 2h - 80 , which is what Scott had