Question

The annual number of burglaries in a town rose by 50% in 2012 and fell by 10% in 2013. hence the total number of burglaries increased by 40% over the two year period.
a. by what percent has the number of burglaries actually changed in the two-year period?
b. by what percent would the crime have to decrease in the second year in order for the change over the two-year period to actually be a 40% increase?

Answer 1

Answer:

a) 35%

b) 6.67%

Step-by-step explanation:

a) The annual number of burglaries in 2012 would be 150% and since in 2013, it fell by 10%:

10% of 150 is 15 so 150-15 = 135%.

The actual percentage increase of burglaries is 135% - 100% = 35% not 40%.

b) In the second year, the percentage would have to decrease by 10% of the initial 150% so $\frac{10}{150}$ = $\frac{1}{15}$ which as a percentage would be 6.66666....% or 6.67%.