I'm looking for some help on some word problems. I need to pass the pre interview police exam. Any help would be greatly appreciated! I'm also willing to pay for online tutoring! ( I use to be pretty good at math, but you know what happens when you don't use math on a regular basis!)
Here are a couple of examples.
Two boxes are put together to increase the storage area for drugs in an apartment. The criminal is storing small boxes of crack measuring 4 cm x 4 cm x 10 cm. How many boxes can fit into the larger box, which measures 1 metre x 1 metre x 0.2 metres?
Without considering arrangement inside the bigger box, or by volumes only,
Volume, V1, of one box of crack = (4cm)(4cm)(10cm) = 160 sq.cm./box
Volume, V2, of larger box = (100cm)(100cm)(20cm) = 200,000 sq.cm.
Number of small boxes to fit inside larger box = V2 / V1
= 200,000 / 160 = 1250 boxes. ------------------------answer.
100/4 = 25 ----meaning, 25 small boxes of 4cm side will fit one 1 meter side.
100/4 = 25 ---same as above, for the other 1m side of the larger box.
20/10 = 2 -----2 small boxes of 10cm side will fit exactly into the 0.20m side.
So, number of small boxes = 25(25)(2) = 1250 boxes.
There is an outdoor party going on in your town. There are 350 people attending. A dangerous storm is 2 hours away and moving at 35 mph towards the festivities. If 100 people can be moved to safety in 30 minutes, how long would it take to evacuate the entire party population?
100people / 30minutes = 10people per 3minutes.
So if there are 350 people total,
(350people)*(3min/10people) = 350*3 / 10 = 105 minutes to evacuate all.
Or, another way,
In 30min, 100people are evacuated.
In 60min, (100 +100) = 200 people evacuated.
In 90min, (100 +100 +100) = 300 people evacuated.
So only 50 people left. How many minutes to evacuate those 50 people?
50 is half of 100, so half of 30min is 15min.
Hence, for 350people, 30+30+30+15 = 105min.
What about the storm that is 2 hours away and moving at 35mph?
No need. Extraneous information.
Well, 2 hours is 2(60) = 120 minutes away. So the 350 people can be evacuated easily before the storm arrives. But the Problem did not ask for that.
The income tax rate is 22%. Each dependent an officer claims reduces the tax rate by 0.5%. The officer makes $68,000 per year gross. If the officer has three children, what will her monthly take home pay be?
Three children as her dependents (the husband is not a dependent here, I assume), so,
effective tax rate = 22% -3(0.5%) = 20.5%
tax = $68,000 *(0.205) = $13,940
take-home pay = $68,000 -$13,940 = $54,060 ------answer, not. This take-home pay in one year.
Edit: monthly pay ---I did not know what the Problem asks for. :-)
Monthly pay = $54,060 / 12 = $4,505 -------------------------------answer.
Solving word problems is usually using "common sense" or reasoning only on the relationships of the given facts. It is very important, though, that you know or understand what the Problem is asking you to find. What it does not ask, don't bother.