SOLUTION: Ned�s bookstore in Berkeley made a profit of $1137.70 when 71 students bought textbooks at the store. When 86 students bought textbooks, they made a profit of $1488.70. a) W

Question 828718: Ned�s bookstore in Berkeley made a profit of $1137.70 when 71 students bought textbooks at the
store. When 86 students bought textbooks, they made a profit of $1488.70.
a) Write a linear function P(x) relating profit to the number of students.
b) What is the variable profit for the store? What is the fixed cost?
c) How many students need to shop at Ned�s for the store to �break even� (profit of $0)?
Found 2 solutions by josgarithmetic, TimothyLamb:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
The description contains two ordered pairs of points.
(students, profit):
(71,1137) and (86,1488.7).

The two points define a line. Slope-intercept form is , and solving for b gives . Compute the slope, m. Use either point to compute b. Now restate the equation for the line using m and b values found. In your example, you want . Do all that and you have answer for (a).

(b) seems unclear, but it may be directly related to or the same as (c). Question part (c) essentially is asking for the x intercept.

Back to (b) again, the variable profit should be P(x). This is a variable. I FEEL that "fixed cost" is the y-intercept.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
---
given:
71, 1137.70
86, 1488.70
---
to solve the linear equation, copy and paste this (the two given points):
71, 1137.70, 86, 1488.70
into the "Two-Point form: x1 y1 x2 y2" input box here: https://sooeet.com/math/linear-equation-solver.php
---
x-intercept = (22.3803419, 0)
y-intercept = (0, -523.7)
slope = 23.4
---
answer:
the slope-intercept form of the linear model for profit analysis at Ned's:
p(x) = 23.4x - 523.7
---
answer:
average variable revenue during this profit analysis time period = $23.40 per student
---
answer:
fixed cost during this profit analysis time period = $523.70
---
break-even point:
p(x) = 23.4x - 523.7 = 0
23.4x = 523.7
x = 523.7/23.4
x = 22.380341880341884
---
answer:
Ned's requires about 23 students to shop during the time period of this profit analysis, (the time period isn't given in the problem statement), in order to break-even for that time period.
---
NOTE:
typical time periods for a profit analysis would be: one day, one week, or one month.
---
Solve and graph linear equations:
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---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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