1. Table of Contents Topic Page #... 3.4B Many or No Solution33 3.8A Solving Equations35 3.8B Solving Formulas37 6.5 Absolute Value Equations39 3.5/3.6 Ratios and Proportions41

2. #41 3.5/3.6 Ratios and Proportions

3. Ratio: Relation between 2 numbers a:b abab a to b

4. You always have to write ratios in the simplest form. You never write the answer as a mixed fraction

5. Ex 1: Cell phone A person makes 6 long distance calls and 15 local calls in 1 month. a. Find the ratio of long distance calls to local calls. 6 15 = 2525

6. Ex 1: Cell phone A person makes 6 long distance calls and 15 local calls in 1 month. b. Find the ratio of local calls to long distance calls 15 6 = 5252

7. Ex 1: Cell phone A person makes 6 long distance calls and 15 local calls in 1 month. c. Find the ratio of long distance calls to all calls. 6 21 = 2727

8. Ex 2: Sports A volleyball team plays 14 home matches and 10 away matches. a. Find the ratio of home matches to away matches. 14 10 = 7575

9. Ex 2: Sports A volleyball team plays 14 home matches and 10 away matches. b. Find the ratio of home matches to all matches. 14 24 = 7 12

10. Ex 2: Sports A volleyball team plays 14 home matches and 10 away matches. c. Find the ratio of away matches to all matches. 10 24 = 5 12

11. Proportions: When two ratios are equal (bd) ad = bc

12. Cross multiply ad = bc

13. Ex #3: Solve. 6k = 90 6 k = 15

14. 4x4x= 36 4 x = 9 Ex #3: Solve.

15. 1 3 x = 9 Reduce around the box 4x4x= 36 4 x = 9

16. 8t8t = 120 t = 15 13 t = 15

17. y =9 y = 9

18. 3(x + 8)= 6x6x 8 = x 3x + 24 = 6x 24 = 3x x = 8 12 2x = x + 8

19. 24(x – 12)= 8x8x 18 = x 24x – 288 = 8x –288 = –16x x = 18 3 1 3x – 36 = x 2x – 36 = 0 2x = 36

20. Ex #4: Architect An architect creates a scale model of a school. The school is 50 feet high. The ratio of the model to the actual school is 1 foot to 75 feet. Estimate the height of the model.

21. 23 3h = 2 h =

22. Ex #5: A map has a scale factor of 1cm : 15km. If the distance of the map is 6cm, find the actual distance. x =

23. Ex #6: Write the sentence as a proportion and solve. 1 4 x =

24. Ex #6: Write the sentence as a proportion and solve. 1 4 x = 1 2