1. Sec 3.5 Increase and Decrease Problems Objectives –Learn to identify an increase or decrease problem. –Apply the basic diagram for increase or decrease problems. –Use the basic percent formula to solve increase or decrease problems.

2. Increase Problems The part equals 100% of the base plus some portion of the base.

3. Increase Problems The part equals 100% of the base plus some portion of the base. Phrases such as after an increase of,

4. Increase Problems The part equals 100% of the base plus some portion of the base. Phrases such as after an increase of, more than,

5. Increase Problems The part equals 100% of the base plus some portion of the base. Phrases such as after an increase of, more than, or greater than

6. Increase Problems The part equals 100% of the base plus some portion of the base. Phrases such as after an increase of, more than, or greater than often indicate an increase problem.

7. Increase Problems The part equals 100% of the base plus some portion of the base. Phrases such as after an increase of, more than, or greater than often indicate an increase problem. The basic formula for an increase problem is:

8. Increase Problems The part equals 100% of the base plus some portion of the base. Phrases such as after an increase of, more than, or greater than often indicate an increase problem. The basic formula for an increase problem is: Original value + Increase = New Value

9. Example 1 BaseRate of Part Inc. (after Inc.) ????20%$660 Base plus some portion of the base equals $660.

10. Base ????

11. Base ???? Amt. Of Increase

12. Base ???? Amt. Of Increase 20% of Base

13. Base ???? Amt. Of Increase 20% of Base Sum of Base and increase is $660

14. Part Rate of Base (after Inc.) Inc. $660 20% ??? 100% of Base + 20% of Base = $660

15. 120% of Base = $660

16. 100% of Base + 20% of Base = $660 120% of Base = $660 R x B = P

17. 100% of Base + 20% of Base = $660 120% of Base = $660 R x B = P Hence, R = 120% P = $660 B = ???

18. R x B = P Hence, R = 120% P = $660 B = ??? Thus, P $660 $660 B = ----- = ---------- = ----------- = $550 R 120% 1.2 So if we take 100% of the base ($550) + 20% of the base ($110) we get $660 (part).

19. Decrease Problems The part equals 100% of the base minus some portion of the base.

20. Decrease Problems The part equals 100% of the base minus some portion of the base. Phrases such as after a decrease of,

21. Decrease Problems The part equals 100% of the base minus some portion of the base. Phrases such as after a decrease of, less than,

22. Decrease Problems The part equals 100% of the base minus some portion of the base. Phrases such as after a decrease of, less than, or after a reduction of

23. Decrease Problems The part equals 100% of the base minus some portion of the base. Phrases such as after a decrease of, less than, or after a reduction of often indicate a decrease problem.

24. Decrease Problems The part equals 100% of the base minus some portion of the base. Phrases such as after a decrease of, less than, or after a reduction of often indicate a decrease problem. The basic formula for a decrease problem is:

25. Decrease Problems The part equals 100% of the base minus some portion of the base, yielding a new value. Phrases such as after a decrease of, less than, or after a reduction of often indicate a decrease problem. The basic formula for a decrease problem is: Original Value - Decrease = New Value

26. Example 2 The sale price of a new Palm Pilot, after a 15% decrease, was $98.38. Find the price of the Palm Pilot before the decrease.

27. Example 2 BaseRate of Part Dec. (after Dec.) ??? 15% $98.38 Base minus some portion of the base equals $98.38.

28. Price Paid = $98.38 (Part)

29. Price Paid = $98.38 (Part) Amt. of Decrease

30. Price Paid = $98.38 (Part) Amt. of Decrease 15% of Base

31. Price Paid = $98.38 (Part) Amt. of Decrease 15% of Base Orig. Price minus decrease = price paid

32. BaseRate of Part Dec. (after Dec.) ??? 15% $98.38 100% of Base - 15% of Base = $98.38

33. 85% of Base = $98.38

34. R x B = P

35. 85% of Base = $98.38 R x B = P Hence, R = 85% P = $98.38 B = ???

36. 85% of Base = $98.38 R x B = P Hence, R = 85% P = $98.38 B = ??? Thus, P $98.38 $98.38 B = ----- = ---------- = ----------- = $115.74 R 85% 0.85 So, if we take 100% of the base ($115.74) minus 15% of the base ($17.36) we get $98.38.

37. Homework Sec 3.5: 1, 3, 5, 7, …, 33