CS-Algebra HTDP Exercise 2.3.3 and Linear Equations

DESIGN RECIPE FOR SOLVING PROBLEMS

I. Data Analysis    
PURPOSE
Find income profit for a theater where each ticket costs each attendee $5. Every show costs the theater $20 per show plus $0.50 per attendee for their overhead.

DATA
Constants: Ticket - $5, Overhead $20 + $0.50 per attendee
Independent Variable: Number of attendees for one show
Dependent Varable: Total Profit

CONTRACT - PURPOSE - HEADER
;;total-profit: Number -> Number
;;Compute how much income profit is produced given the number of attendees per show.
(define (total-profit attendees) ... )
    
II Examples
Header Attendees Profit    
Data Examples 10 5 * 10 - (20 + .50 * 10) = 50 - 25 = 25    
Pick easy "head" data that has a pattern. 20 5 * 20 - (20 + 50 * 20) = 100 - 30 = 70    
30 5 * 30 - (20 + 50 * 30) = 150 - 35 = 115    
Variable A 5 * A - (20 + 50 * A ) = P    
Combine Like Terms   5A - 20 + 1/2A = P    
Slope-Intercept Form   P = 9/2A - 20    
III. BODY    
( - ( * 5 attendees) (+ 20 ( * 0.5 attendees)))
    
IV TEST    
(total-profit 10) = 25
(total-profit 20) = 70
(total-profit 30) - 115
        
Algebra Connection Write Equation of Line given (10, 25) (20, 70) (30, 115) X Y
Y = 9/2 X + B   Change in Y = 45 10 25
25 = 9/2 (10) + B   Change in X = 10 20 70
25 = 45 + B   m = 45 / 10 m = 9/2 30 115
B = - 20   Y = 9/2X - 20    
         
Excel does not plot points so you do it.
X-axis Domain is the attendees. Y-axis Range is the profit.
Look at the slope and Y-intercept. Do you see the connection?

Excel Chart ChartObject Y = 9/2X - 20


Last Updated on 12/9/04
By North