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Solve in 2 minutes

by ssmiles08 » Sat May 30, 2009 5:15 am
It took me around 3 1/2 minutes to solve this one with all the heavy multiplication. Anyone can solve it in a easier approach?

The 84 workers at a certain plant are either semi-skilled or skilled. Semi-skilled earn 12,000 per year while skilled workers earn 18,000 per year. If each worker in the plant is given a productivity bonus equal to 3% of their annual wage, and the total amount of money awarded in these bonuses was 32,760 what percent of the workers are skilled?

(A) 8%
(B) 16 2/3%
(C) 20%
(D) 25%
(E) 33 1/3%

OA: [spoiler](B)[/spoiler]
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by truplayer256 » Sat May 30, 2009 6:16 am
Took me about 1 and a half minutes but I don't know if this is the same thing that you did to solve the problem.

3% of $12,000 is 360 and 3% of $18,000 is $540. Now set up an equation:
360(x)+540(84-x)=32,760
360(x)+45,360-540(x)=32,760
45,360-180x=32,760
x=70

Amount of skilled workers= 84-70=14

14/84*100=16.67% B
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Re: Solve in 2 minutes

by dtweah » Sat May 30, 2009 7:08 am
ssmiles08 wrote:It took me around 3 1/2 minutes to solve this one with all the heavy multiplication. Anyone can solve it in a easier approach?

The 84 workers at a certain plant are either semi-skilled or skilled. Semi-skilled earn 12,000 per year while skilled workers earn 18,000 per year. If each worker in the plant is given a productivity bonus equal to 3% of their annual wage, and the total amount of money awarded in these bonuses was 32,760 what percent of the workers are skilled?

(A) 8%
(B) 16 2/3%
(C) 20%
(D) 25%
(E) 33 1/3%

OA: [spoiler](B)[/spoiler]
This problem Must have 2 equations (which you can turn into one)and their is no simple way to avoid those two equations. The number of people and the total amount of bonus they received are two separate quantities. You need informatin from both to solve. The speed you seek may be:

1. Speed of solving ANY Linear System or its transformation once you formulate it. Some could take 1 min others 2min whle others 3. So if you can take 1 minute to read a problem and figure it has a linear system and can formulate that system in 1, are able to solve any linear equation in 2 variables in 1 or less minute, the problem above can be solved in under 2 minutes. Otherwise, it will be over two.

2. Speed of Reducing Big Numbers to Small ones, speed of division.

Lets put some time on each process:

Reading Whole problem: 15 Seconds

Rereading, First sentence give away one equation in 2 unknowns. You are thinking there must be a second equation in 2 unknown hidden in 2nd part.

X+Y = 84 (5)sec.

You plunge immediately in second part to figure 2nd equation.
Figuring and Organizing:

12000 x 3/100 X + 18000 x 3/100 x Y=32,760 (30 Sec)

Reducing to simplest form

2x + 3y=182 (20)Secs.

70 Seconds Gone.

From this point on, Some might take an additional 1 min to figure out Y, while others might take 2 mins, while still others might take less than 30 secs.

Let's see how we could solve Y in 15 seconds

2X +2Y +Y = 182
2(X+Y) +Y =182
2(84)+Y=182
168+Y=182
Y=14 15 Sec
14/84 =16 2/3%

70 Sec +15Sec=85 Sec<120Sec
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by ssmiles08 » Sat May 30, 2009 8:04 am
Yup reading and re-reading and setting up the equations took up half my time. I guess the only way to do that is get familiar with these types of word problems.

Thanks guys!
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