Question

Since the enactment of a smoking ban in a particular​ city, the number of smokers has slowly declined. Statistics show that the number of smokers in this city has decreased for four consecutive months by​ 3%, 2%,​ 5%, and​ 2%. What was the overall percentage decrease in the number of smokers during this four month​ period? Round your answer to the nearest tenth of a percentage point.

Answer 1

Answer:

11.5%

Step-by-step explanation:

Let the number of smokers before ban = 100

Decrease in 1st month = 3% , of 100 = 3

Smokers after 1st month = 100 - 3 = 97

Decrease in 2nd month = 2%, of 97 = 1.94

Smokers after 2nd month = 97 - 1.94 =  95.06

Decrease in 3rd month = 5%, of 95.06 = 4.75

Smokers after 3rd month = 95.06 - 4.75 = 90.31

Decrease in 4th month = 2%, of 90.31 = 1.80

Smokers after 4th month = 90.31 - 1.80 = 88.51

• Decrease in smokers after 4th month = (Decrease / old value) x 100

[ (100 - 88.51) / 100 ] x 100 = (11.49 / 100) x 100

= 11.5%