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. |
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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 | ||||
IV TEST | ||||
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? |