kaplan word problem

resilient · Posted: Tue Mar 18, 2008 11:09 am Post subject: kaplan word problem

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

a. 8%
b.16.667%
c. 20%
d. 25%
e. 33.333%

qa is B, I am getting lost on setting up the equations and making this much harder than it should be! Help Stuart?

xilef · Posted: Tue Mar 18, 2008 11:50 am Post subject:

skilled- A
semi skilled - B

A bonus = 540
B bonus = 360

1st eq:
540A+360B=32760 => 3A+2B=182

2nd eq:
A+B=84

solving for A:

3A+2(84-A)=182
3A+168-2A=182
A=14 which is 16.6% of 84

Answer is B

2008nv · Posted: Tue Mar 18, 2008 11:56 am Post subject:

semiskilled - X
skilled- Y

X+Y=84
12000*0.03*X+18000*0.03*Y=32760

360*X+540*Y=32760 | (: 10)
36*X+54*Y=3276

X=84-Y
36*(84-Y) + 54*Y = 3276
3024 - 36*Y +54*Y=3276
18*Y=252
Y=14

(14/84)*100=16.667 %

resilient · Posted: Wed Mar 19, 2008 8:04 am Post subject: how easy

this is much easier than i thought. The real challenge is just getting the words into an equation. I think I made this question much harder than it really is!