Sec 3.5 Increase and Decrease Problems

Sec 3.5 Increase and Decrease Sec 3.5 Increase and Decrease ProblemsProblems

• 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.

Increase ProblemsIncrease Problems

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



Phrases such as after an increase of,



Phrases such as after an increase of, more than,



Phrases such as after an increase of, more than, or greater than



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:




The basic formula for an increase problem is:Original value + Increase = New Value

Example 1Example 1Base Rate of Part

Inc. (after Inc.)???? 20% $660

Base plus some portion of the base equals $660.

Base????

Base????

Amt. Of Increase

Base????

Amt. Of Increase20% of Base

Base????

Amt. Of Increase20% of Base

Sum of Baseand increase is

$660

Part Rate of Base(after Inc.) Inc.

$660 20% ???

100% of Base + 20% of Base = $660

100% of Base + 20% of Base = $660

120% of Base = $660

100% of Base + 20% of Base = $660

120% of Base = $660 R x B = P

100% of Base + 20% of Base = $660

120% of Base = $660 R x B = PHence, R = 120% P = $660 B = ???

R x B = PHence, R = 120% P = $660 B = ??? Thus, P $660 $660B = ----- = ---------- = ----------- = $550 R 120% 1.2

So if we take 100% of the base ($550) + 20% of the base ($110) we get $660 (part).

Decrease ProblemsDecrease Problems

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



Phrases such as after a decrease of,



Phrases such as after a decrease of, less than,



Phrases such as after a decrease of, less than, or after a reduction of



Phrases such as after a decrease of, less than, or after a reduction of often indicate a decrease problem.



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:


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

ExampleExample 2 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.

ExampleExample 2 2

Base Rate of Part Dec. (after Dec.)

??? 15% $98.38

Base minus some portion of the base equals $98.38.

Price Paid = $98.38(Part)


Amt. of Decrease


Amt. of Decrease15% of Base


Amt. of Decrease15% of Base

Orig. Price minus decrease = price paid

Base Rate of Part Dec. (after Dec.)

??? 15% $98.38

100% of Base - 15% of Base = $98.38

100% of Base - 15% of Base = $98.38

85% of Base = $98.38

85% of Base = $98.38 R x B = P

85% of Base = $98.38 R x B = P

Hence, R = 85% P = $98.38 B = ???

85% of Base = $98.38 R x B = P

Hence, R = 85% P = $98.38 B = ???Thus, P $98.38 $98.38B = ----- = ---------- = ----------- = $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.

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

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Sec 3.5 Increase and Decrease Problems