Respuesta :
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%.
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