# 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

Last Updated on 12/9/04
By North