Word Problem in Finite Math

Question

In a town, 40% of the men and 30% of the women are overweight. If the town has 46% men and 54% women, what percent of the people are overweight?

Answer 1

 

Let us say that there are x men, y women

 

total = x + y

 

Since 46 percent of people are men, number of men/total people = 46/100

in other words,

x / (x+y) = 46/100 => 46x + 46y = 100x , or 54x = 46y or x = 46/54y .... we will need this later

 

40 percent of men are overweight => 40/100 x 

 

similarly 30 percent of women are overweight => (implies) 30/100 y are overweight

 

Therefore, total number of people overweight = 40/100 x  + 30/100 y => 0.4x + 0.3y

 

percentage of people that are overweight is

total number of people overweight/total population x 100

 

i.e. percent of people that are overweight = 0.4x + 0.3y / (x+y) x 100 . 

 

Substituting x in the above equation, we get 

 

percent of people overweight = (0.4*46/54y + 0.3y) / (46/54y + y) x 100 => y(0.4 + 46/54)/y(46/54 + 1) * 100

 

we can remove y from the equation, since it occurs in both the numerator and denominator (24/24 = 1, 47/47 = 1, and so on)

 

Therefore, the percent of people that are overweight = (0.4*46/54 + 0.3) / (46/54 + 1) * 100 => 0.6407/1.852 * 100

or around 34.6% of the population is overweight