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College Algebra K /DC Wednesday, 23 April 2014

College Algebra K /DC Wednesday, 23 April 2014. OBJECTIVE TSW solve applications of linear systems. Pick up papers from the front. ASSIGNMENT DUE Sec. 5.1: p. 506 (47-52 all)  I will collect ASSIGNMENT DUE FRIDAY Sec. 5.1: pp. 508-509 (89-93 all )  today’s assignment

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College Algebra K /DC Wednesday, 23 April 2014

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  1. College Algebra K/DCWednesday, 23 April 2014 OBJECTIVE TSW solve applications of linear systems. Pick up papers from the front. ASSIGNMENT DUE Sec. 5.1: p. 506 (47-52 all) I will collect ASSIGNMENT DUE FRIDAY Sec. 5.1: pp. 508-509 (89-93 all) today’s assignment QUIZ FRIDAY, 04/25/2014 Sec. 5.1 only.

  2. Systems of Linear Equations 5.1 Using Systems of Equations to Model Data

  3. Using a Linear System to Solve an Application • The problems today are applications so complete-sentence answers will be required.

  4. Using a Linear System to Solve an Application • The sum of two numbers is 34, and the difference between the numbers is 8. Find the numbers. Verify: 21 + 13 = 34 21 – 13 = 8 √ √ The two numbers are 21 and 13.

  5. Using a Linear System to Solve an Application • In the 2006 Winter Olympics in Torino, Italy, the two countries winning the most medals were Germany and the United States. The total number of medals won by these two countries was 54, with Germany winning 4 more medals than the United States. How many medals were won by each country? (Source: www.infoplease.com) Let x = the number of medals won by the U.S. Let y = the number of medals won by Germany. Then, we have the system:

  6. Using a Linear System to Solve an Application • Substitute x + 4 for y in equation (1), then solve for x. Substitute 25 for xin equation (2), then solve for y. The U.S. won 25 medals and Germany won 29 medals.

  7. Using a Linear System to Solve an Application • Verify that (25, 29) checks in the words of the original problem. The total number of medals won was 25 + 29 = 54. 29 is 4 more than 25.

  8. Using a Linear System to Solve an Application • The table shows the number of units of protein, fat, and fiber are in one unit of each ingredient in an animal feed. How many units of each ingredient should be used to make a feed that contains 35 units of protein, 38 units of fat, and 28 units of fiber? x y z

  9. Using a Linear System to Solve an Application Since the total amount of protein is to be 35 units, the first row of the table yields The total amount of fat is to be 38 units, so the second row of the table yields Since the total amount of fiber is to be 28 units, the third row of the table yields Let x = the number of units of corn. Let y = the number of units of soybeans. Let z = the number of units of cottonseed.

  10. Using a Linear System to Solve an Application We can convert the decimals to integers in order to make solving easier. To do this, multiply both sides of equation (1) by 100 and both sides of equations (2) and (3) by 10 to obtain the equivalent system

  11. Using a Linear System to Solve an Application Multiply equation (5) by –20, then add the result to equation (4) to eliminate y. Multiply equation (6) by –20, then add the result to equation (4) to eliminate yand z, then solve for x.

  12. Using a Linear System to Solve an Application Substitute 60 for x in equation (7), then solve for z. Substitute 60 for x and 20 for z in equation (6), then solve for y. Verify that the ordered triple (60, 40, 20) satisfies the system formed by equations (1), (2), and (3). The feed should contain 60 units of corn, 40 units of soybeans, and 20 units of cottonseed.

  13. Assignment • Sec. 5.1: pp. 506-509(89-93 all) • Due on Friday, 25 April 2014.

  14. Assignment: pp. 508-509 (89-93 all)Due Friday, 25 April 2014. • Set up a system of equations and use them to solve the problem. Show work. Write answers in complete sentences. • 89) The sum of two numbers is 47, and the difference between the numbers is 1. Find the numbers. • 90) At the Jeb Bush ranch, 6 goats and 5 sheep sell for $305, while 2 goats and 9 sheep sell for $285. Find the cost of a single goat and of a single sheep. • 91) The Fan Cost Index (FCI) is a measure of how much it will cost a family of four to attend a professional sports event. In 2005, the FCI prices for Major League Baseball and the National Football League averaged $250.51. The FCI for baseball was $158.62 less than that of football. What were the FCIs for these sports? (Source: Team Marketing Report, Chicago)

  15. Assignment: pp. 508-509 (89-93 all)Due Friday, 25 April 2014. • Set up a system of equations and use them to solve the problem. Show work. Write answers in complete sentences. • 92) A cashier has a total of 30 bills, made up of ones, fives, and twenties. The number of twenties is 9 more than the number of ones. The total value of the money is $351. How many of each denomination of bill are there? • 93) A sparkling-water distributor wants to make up 300 gal of sparkling water to sell for $6.00 per gallon. She wishes to mix three grades of water selling for $9.00, $3.00, and $4.50 per gallon, respectively. She must use twice as much of the $4.50 water as the $3.00 water. How many gallons of each should she use?

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