Question

The number of private investigators is expected to increase from 52,000 in 2006 to 61,000 in 2016. If there are 648,982 police

officers in 2006, how many police officers must there be in 2016 to have a greater percent increase than that of private
investigators?
a. 657,983
b. 761,307
C. 671,128
d. 713 180
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Answer 1

Option b. 761,307

Explanation:

step 1

Find the percent increase of private investigators

we know that

52,000 -----> represent 100%

so

using proportion

Find out the percent increase of (61,000-52,000=9,000) private investigators

Let

x -----> the percent increase

`(52,000)/(100\%)= (9,000)/(x\%)\\\\x=9,000*100/52,000\\\\x=17.3\%`

step 2

Find the number of police officers for a percent increase of 17.3%

we know that

648,982 ----> represent 100%

`100\%+17.3\%=117.3\%=117.3/100=1.173\\1.173(648,982)=761,256`

Remember that

To have a greater percent increase than that of private

investigators, the number of police officers must be greater than 761,256

therefore

The best answer is 761,307