How many students have brown hair?

Question

1/5 have brown hair and 2/7 have blonde hair. The rest have black and red hair in ratio of 4:5. 220 have red hair. How many have brown hair?

Answer 1

Let x = the total number of students:

• Brown Hair = (1/5)x = x/5
• Blond Hair = (2/7)x = 2x/7
• Brown + Blond = x/5 + 2x/7 = 7x/35 + 10x/35 = 17x/35

 

So the "rest", who have black and red hair, are 1 - 17x/35 = 18x/35.  5/9 of those have red hair, and there are 220 red haired students:

 

(18x/35)(5/9) = 220

 

Solve for x.  The number of brown haired student = x/5.