1. 4.3 Application problems dealing with systems of linear equations

2. UP and DOWN the River A boat averages 35 miles per hour with the current and 28 miles per hour against the current. What would the boats speed be in still water? I know you can figure it out, but let’s practice the algebra!

3. UP and DOWN the River Let s = the speed of the boat Let c = the current speed Speed of boat with currents + c = 35 Speed of boat against the currents – c = 28 Add the two equation together and solve for s.

4. UP and DOWN the River After adding you have Thus, s = 31.5 mph

5. Two Angles Problem If two angles are complementary (sum = 90 degrees), and the larger angle is 20 less than 3 times the smaller angle, find the two angles.

6. Two Angles Problem Let x = the small angle Let y = the larger angle Also, y = 3x -20

7. Two Angles Problem

8. Use substitution to solve Thus,

9. Two Angles Problem Now solve this for x, and then find both of the angles

10. Two Angles Problem 27.5 62.5 Is the total 90?

11. $$ SALARY not Celery $$ John, a car sales man, earns a weekly rate plus commission on sales all his sales. In week one his salary was $1000 on $40,000 sales. The next week his salary was $1120 on $52,000 sales. What is John’s commission rate and weekly salary?

12. $$ SALARY not Celery $$ Salary = weekly pay + (sales)(commission %) Let x = the weekly pay Let y = the commission Week 1: 1000 = x + (40000)(y) Week 2: 1120 = x + (52000)(y)

13. $$ SALARY not Celery $$ Week 1: 1000 = x + (40000)(y) Week 2: 1120 = x + (52000)(y) Solve using the addition method!

14. $$ SALARY not Celery $$ Week 1: 1000 = x + (40000)(y) Week 2: 1120 = x + (52000)(y) Multiply Week 2 by (-1) Thus, Week 1: 1000 = x + 40000y Week 2: -1120 = -x + -52000y Now add the two equation together, and…..

15. $$ SALARY not Celery $$ Solve for y and remember what y represents, then use substitution to solve for x.

16. $$ SALARY not Celery $$ So, the commission rate is 1% and Week 1: 1000 = x + 40000(1%) Solve for x (weekly pay).

17. $$ SALARY not Celery $$ Week 1: 1000 = x + 40000(1%) Solve for x (weekly pay). X = 600 (weekly pay)

18. Solution mixture problem A weed killer with an active ingredient of 24% is to be mixed with water (0%) to make a 100 gallon mixture with 18% active ingredient. How much of each should be added?

19. Solution mixture problem Let x = Gallons of Weed killer (24%) Let y = Gallons of Water (0%) Why.18 here?

20. Solution mixture problem Solve #2 for x and then use #1 to find y #1 #2

21. Solution mixture problem Therefore, 75 gallons of weed killer should be mixed with 25 gallons of water to make 100 gallon mixture with 18% active ingredient.