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T O P I C    R E V I E W
Zubaida Posted - 10/27/2012 : 04:00:12
Some job seeks who have difficulty finding new employees are described as discouraged workers. The September 6, 2003, issue of The New York Times reported that losses were mounting. In August 2003, the count of discouraged workers rose to 503,000, 2 times as many as in August 2002. How many discouraged workers were there in August 2002?

This problem can be solved by using the portion formula (Portion = Base * Rate) in which:
1. Percent of increase (250%) represents the rate (when converting 2, 1/2 to a decimal number, we get: 2.5).
2. The number of discouraged workers in 2002 (which is unknown) represents the base.
3. And the number of discouraged workers in 2003 represents the portion whic is equal to 503,000.
Number of discouraged workers in 2003 (P) = Percent of increase (R) * Number of discouraged workers in 2002 (B)
Next, we substitute in the equation:
503,000 = 2.5B
We solve the equation for B by dividing the number of discouraged workers in 2003 (503,000) by percent of increase 2.5:
B = 503,000 / 2.5
B = 201,200 workers
So, the number of discouraged workers as of August 2002 is workers.

Checking this answer by using the formula of calculation a percent increase:

Percent of increase (R) = Amount of increase (P) / Original number (the number of discouraged workers in 2002) (B)

Percent of increase = (503,000 - 201,200) / 201,000
= 301800 / 201,200
=1.5
1.5 is not equal to 2.5

[size=4]I tried to solve the problem in another way:

This problem can be solved by using the portion formula (Portion = Base * Rate) in which:

1. Percent of increase (250%) represents the rate (when converting 2, 1/2 to a decimal number, we get: 2.5).

2. The number of discouraged workers in 2002 (which is unknown) represents the base.

3. And the amount of increase represents the portion (This one can be known by finding the difference between the number of discouraged workers in 2003 and the number of them in 2002: 503,000 B).
Amount of increase (P) = Percent of increase (R) * Number of discouraged workers in 2002 (B)
Next, we substitute in the equation:
503,000 - B = 2.5B
We solve the equation for B by moving -B with a positive sign to the right side:
3.5B = 503,000
Then, we divide 503000 by 3.5:
B = 503,000 / 3.5
B = 143714.28571428571428571428571429
B = 143,714.3 workers.
So, the number of discouraged workers as of August 2002 is 143,714.3 workers.
Which solution is the correct one?
If both of them are wrong? where is the wrong step?
3   L A T E S T    R E P L I E S    (Newest First)
Zubaida Posted - 11/01/2012 : 17:07:17
Thank you so much for your clear explanation. I completely understand it.
the_hill1962 Posted - 10/30/2012 : 09:41:30
Zubaida:
The way you solved it the first time is correct! The answer is 201,200. Your "check" was not correct. "2.5 times" is not saying "250% increase". 250% increase would be 3.5 times.
You see, 250% increase means to ADD 250% to the original amount. That is, multiply by 2.5 and then add it (increase) to the original amount.
Algebraically, that is 2.5x + 1x and that is how the 3.5x comes about.
Note: royhas showed you the correct way to check the answer.

As for your second approach, that is not correct because of the above explanation of the meaning of percent increase is not the same as just plain multiplication.
royhaas Posted - 10/29/2012 : 08:52:34
503000 = 2.5August2002.

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