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%