PERCENT OF CHANGE WORD PROBLEMS

Problem 1 : 

Amber got a raise, and her hourly wage increased from $8 to $9.50. What is the percent increase?

Solution :

Step 1 :

Find the amount of change. 

Amount of change  =  Greater value - Lesser value 

=  9.50 - 8.00

=  1.50

Step 2 : 

Find the percent increase. Round to the nearest percent.

Percentage change is 

=  (Amount of change / Original amount) ⋅ 100%

=  (1.50 / 8.00) ⋅ 100%

=  0.1875 ⋅ 100%

=  18.75%

≃  19 %

Hence, Amber's hourly wage is increased by 19%.

Problem 2 : 

The price of a pair of shoes increases from $52 to $64. What is the percent increase to the nearest percent?

Solution :

Step 1 :

Find the amount of change. 

Amount of change  =  Greater value - Lesser value 

=  64 - 52

=  12

Step 2 : 

Find the percent increase. Round to the nearest percent.

Percentage change is 

=  (Amount of change / Original amount) ⋅ 100%

=  (12 / 52) ⋅ 100%

=  0.2307 ⋅ 100%

=  23.07%

≃  23%

Hence, the price of a pair of shoes increased by 23%.

Problem 3 : 

In a class, students strength has been increased from 20 to 30. What percent of strength is increased ?

Solution :

Step 1 :

Find the amount of change. 

Amount of change  =  Greater value - Lesser value 

=  30 - 20

=  10

Step 2 : 

Find the percent increase. Round to the nearest percent.

Percentage change is 

=  (Amount of change / Original amount) ⋅ 100%

=  (10 / 20) ⋅ 100%

=  0.5 ⋅ 100%

=  50%

Hence, the strength is increased by 50%. 

Problem 4 : 

Mr. David monthly salary is revised from $2500 to $2600. What percentage is the salary increased ?

Solution :

Step 1 :

Find the amount of change. 

Amount of change  =  Greater value - Lesser value 

=  2600 - 2500

=  100

Step 2 : 

Find the percent increase. Round to the nearest percent.

Percentage change is 

=  (Amount of change / Original amount) ⋅ 100%

=  (100 / 2500) ⋅ 100%

=  0.04 ⋅ 100%

=  4%

Hence, David's monthly salary is increased by 4%.

Problem 5 : 

David moved from a house that is 89 miles away from his workplace to a house that is 51 miles away from his workplace. What is the percent decrease in the distance from his home to his workplace ?

Solution :

Step 1 :

Find the amount of change. 

Amount of change  =  Greater value - Lesser value 

=  89 - 51

=  38

Step 2 : 

Find the percent decrease. Round to the nearest percent.

Percentage change is 

=  (Amount of change / Original amount) ⋅ 100%

=  (38 / 89) ⋅ 100%

=  0.427 ⋅ 100%

=  42.7%

≃  43%

Hence, the percent decrease in the distance from his home to his workplace is 43%.

Problem 6 : 

The number of students in a chess club decreased from 18 to 12. What is the percent decrease ? Round to the nearest percent.

Solution :

Step 1 :

Find the amount of change. 

Amount of change  =  Greater value - Lesser value 

=  18 - 12

=  6

Step 2 : 

Find the percent decrease. Round to the nearest percent.

Percentage change is 

=  (Amount of change / Original amount) ⋅ 100%

=  (6 / 18) ⋅ 100%

=  0.3333 ⋅ 100%

=  33.33%

≃  33%

Hence, the strength is decreased by 33%. 

Problem 7 : 

Officer Brimberry wrote 16 tickets for traffic violations last week, but only 10 tickets this week. What is the percent decrease ?

Solution :

Step 1 :

Find the amount of change. 

Amount of change  =  Greater value - Lesser value 

=  16 - 10

=  6

Step 2 : 

Find the percent decrease. Round to the nearest percent.

Percentage change is 

=  (Amount of change / Original amount) ⋅ 100%

=  (6 / 16) ⋅ 100%

=  0.375 ⋅ 100%

=  37.5%

≃  38%

Hence, the percentage decrease is 38%. 

Problem 8 : 

Over the summer, Jackie played video games 3 hours per day. When school began in the fall, she was only allowed to play video games for half an hour per day. What is the percent decrease? Round to the nearest percent

Solution :

Step 1 :

Find the amount of change. 

Amount of change  =  Greater value - Lesser value 

=  3 - 0.5

=  2.5

Step 2 : 

Find the percent decrease. Round to the nearest percent.

Percentage change is 

=  (Amount of change / Original amount) ⋅ 100%

=  (2.5 / 3) ⋅ 100%

=  0.8333 ⋅ 100%

=  83.33%

≃  83%

Hence, the percentage decrease is 83%. 

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