Expressions in terms of x and y

Question

At a company there are x male applicants and y female applicants. After all the interviews the company ends up hiring 16% of the male applicants and 15% of the female applicants. Write expressions in terms of x and y for the following quantities:

 

a) The total number of applicants

 

b) The total number of applicants the company decided to hire

 

c) The percentage of applicants that were accepted

Answer 1

a) Let's call the total number of applicants N. If you add the male and female applicants together, you get all of the applicants.

 

N = x + y

 

b) Let's call the number of successful applicants H. Now, 15% equals 15/100, or, in decimal form, .15. Translating the mathematical problem: "15% of the female applicants" means you take .15 of y. "Of" tends to refer to multiplication in a word problem. 

 

H = .16x + .15y

 

c) This is thankfully fairly easy to do given the answers we got in a) and b).

If we want to know the fraction of applicants that made it, we should divide the number successful by the number total. (I decided to call the expression F on a bit of a whim)

 

F = (Number successful)/(Number total)

F = (H)/(N)

F = (.16x + .15y)/(x+y)

 

To convert any fraction into a percent, you multiply that fraction by 100, and then add the lovely % sign.

 

% accepted = 100(.16x+.15y)/(x+y) %