111 people are in a school.
¹₃ of the males and
¹₅ of the females wear glasses.
33 people wear glasses.

1. How many males are there?
2. How many females are there?
3. How many people do not wear glasses?

	Number	Males	Females
Total	111	3 u	5 p
Wear glasses	33	1 u	1 p
No glasses		2 u	4 p

(a)
Number of males = 3 u
Number of females = 5 p

3 u + 5 p = 111 --- (1)
1 u + 1 p = 33 --- (2)

(2) _{x 3}
3 u + 3 p = 99 --- (3)

(1) - (3)
(3 u + 5 p) - (3 u + 3 p) = 111 - 99
3 u + 5 p - 3 u - 3 p = 12
2 p = 12

1 p = 12 ÷ 2 = 6

Substitute 1 p = 6 into (2).

1 u + 1 p = 33
1 u + 6 = 33

1 u = 33 - 6 = 27

Number of males
= 3 u
= 3 x 27
= 81

(b)
Number of females
= 5 p
= 5 x 6
= 30

(c)
Number of males who do not wear glasses
= 3 u - 1 u
= 2 u

Number of females who do not wear glasses
= 5 p - 1 p
= 4 p

Number of people who do not wear glasses
= 111 - 33
= 78

Answer(s): (a) 81; (b) 30; (c) 78