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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?

Sagot :

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 [tex]\frac{10}{150}[/tex] = [tex]\frac{1}{15}[/tex] which as a percentage would be 6.66666....% or 6.67%.

The number of burglaries actually changed in the two-year period will be 35% and 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 will be 6.7%

Burglaries

It is act of breaking and entering a dwelling at night to commit a felony such as theft.

How to solve this problem?

The steps are as follow:

  • Let us assume that the annual number of burglaries in 2011 are 100.
  • After that there is 50% increase in 2012 so the number of burglaries will be: 100(1.50) = 150.
  • Burglaries after the 10% reduction in 2013 would be: 150(.90) = 135
  • So there will be change in burglaries over the two-year period = (135 / 100) - 1 = 35%
  • To know how much burglaries would have to reduce in order to have a 40% change in burglaries we would be using the following formula:

(x - 100) / 100 = 0.40

x - 100 = 40

x = 140

  • Change in burglaries over the two-year period to have 40% increase = (140 / 150) - 1 = 6.7%

So, burglaries after the 10% reduction in 2013 would be 35% and change in burglaries over the two-year period to have 40% increase will be 6.7%.

Learn more about burglaries here:

https://brainly.com/question/6203610

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