Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Solve Linear Equations Algebraically Chapter 9

Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Model an IMAX Screen IMAX Theatres are found in many cities, such as Vancouver, Edmonton, and Winnipeg. The perimeter of the screen is 76 m. The width of the screen at the theatre in Winnipeg is 6 m more than the height. IMAX is a Canadian invention. The first IMAX theatre opened in 1971 at Ontario Place in Toronto. Did You Know? Determine the height and width of the screen.

Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Let the height of the screen be represented by h. Write a System of Equations Let the width of the screen be represented by w. The width is 6 m longer than the height. The perimeter is 76 m. Model an IMAX Screen w h

Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Solve the System of Equations by Substitution Substitute the expression h + 6 from equation 1 for the variable w in equation 2. Solve for h Model an IMAX Screen

Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Substitute the value of h into equation 1. The solution is h = 16 and w = 22. There are currently about 320 IMAX theatres operating in 42 countries. Did You Know? 1 Model an IMAX Screen Solve the System of Equations by Substitution

Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Substitute h = 16 and w = 22 in the original equations. The solution h = 16 and w = 22 is correct. Verify the Solution Model an IMAX Screen The height of the screen is 16 m, and the width is 22 m.

Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. The IMAX theatre in Winnipeg has 276 seats. All tickets were sold for an evening performance for gross box office receipts of $3104. Tickets for a major 3D feature cost $12 for ages 14 to 59 and $10 for children under 14 or seniors over 59. How many tickets were sold at each price? Model IMAX Ticket Sales

Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Let the number of adult tickets sold be represented by a. Let the number of child/senior tickets sold be represented by c. There are 276 seats in the theatre. The total box office receipts are $3104. Model IMAX Ticket Sales Write a System of Equations

Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Multiply the first equation by 12. Then, subtract the second equation from the first. Model IMAX Ticket Sales × 2 Solve the System of Equations by Elimination

Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Substitute the value for c in one of the original equations, and solve for a. The solution is a = 172 and c = 104. Model IMAX Ticket Sales Solve the System of Equations by Elimination 1

Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Substitute a = 172 and c = 104 in the original equations. The solution a = 172 and c = 104 is correct. Model IMAX Ticket Sales Verify the Solution

Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. The theatre sold 172 adult tickets and 104 child/senior tickets. Model IMAX Ticket Sales State the Solution