finding break-even point

Question

cinema manger graphed weekly profits as a function of the number of patrons and found that the relationship was linear. one week the profit was $11,328 when 1324 patrons attented. another week 1529 patrons produced a profit of $13,275.50. what is the break even point (the number of patrons for which there is zero profit)?

Answer 1

P(p) P(1324) = 11,328, P(1529) = 13,275.50

P(x) = 0 what is x? x=number of patrons that has zero profit, the break even point

each patron added profit = (13275.5-11328)/(1529-1324) = 19/2 = 9.5 = slope of the linear relation. Each patron adds $9.50 in revenue over cost

P=9.5p +b in slope intercept form, y=mx+b with b=y intercept

P(1324) = 9.5(1324) +b = 11,328

b = 11328 - 9.5(1324) = 11,328-12578= -1250

Profit = 9.5p -1250 =0

9.5p = 1250

p = 1250/9.5 = 2500/19 = about 131.58 patrons

break even point is between 131 and 132 patrons

= about 132 patrons rounded up to nearest integer