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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