A percent word problem

by shen
(malaysia)

A factory has 800 workers. 40% of them are females. The management decides to employ more female workers to cope with the increasing demands of the workload such that the total number of females will increase to 60% of the total workforce.

How many new female workers must the factory employ?


Solution

Let x be the number of more female workers that must be hired.


Let 800 + x be the new total workforce


Number of female workers now + x = 60% of the total workforce.

40% of 800 + x = 60% of the total workforce.


40% × 800 + x = 60% of (800 + x)


40% × 800 + x = 60% × (800 + x)


0.40 × 800 + x = 0.60 × (800 + x)


0.40 × 800 + x = 0.60 × 800 + 0.60x


320 + x = 480 + 0.60x


320 - 320 + x = 480 - 320 + 0.60x


x = 160 + 0.60x


x - 0.60x = 160


0.40x = 160


0.40x / 0.40 = 160 / 0.40


x = 400


The company has to hire 400 more female workers.


Number of female workers after hiring more is 320 + 400 = 720

Total number of new workforce is 800 + 400 = 1200


Indeed = 720 / 1200 = 0.6 = 60%


Indeed, 160 + 320 = 480 and 480 / 800 = 0.6 = 60%

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Oct 10, 2022
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by: Jetser

I like it very much when people make such valuable contribution!

Oct 10, 2022
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by: Jetser

Very good observation CJB! Notice how the problem is now solved with algebra.

Oct 26, 2016
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I think this is incorrect
by: CJB

hmm... this seems wrong to me.

Question states:

total number of females will increase TO 60% of the total workforce

the answer given is increasing the female workforce BY 60% (and is not of the total workforce.

workforce: 800
40% female = 320
so, 60% male = 480
if increasing to 60% female, this means male will be 40%
so, 480 males is 40% of new workforce
so must be 60% female = 720
so increase from 320 to 720 means they need to employ 400 females

answer is 400, not 192

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