162 people are in a school.
¹₃ of the females and
¹₈ of the males wear glasses.
44 people wear glasses.

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

	Number	Females	Males
Total	162	3 u	8 p
Wear glasses	44	1 u	1 p
No glasses		2 u	7 p

(a)
Number of females = 3 u
Number of males = 8 p

3 u + 8 p = 162 --- (1)
1 u + 1 p = 44 --- (2)

(2) _{x 3}
3 u + 3 p = 132 --- (3)

(1) - (3)
(3 u + 8 p) - (3 u + 3 p) = 162 - 132
3 u + 8 p - 3 u - 3 p = 30
5 p = 30

1 p = 30 ÷ 5 = 6

Substitute 1 p = 6 into (2).

1 u + 1 p = 44
1 u + 6 = 44

1 u = 44 - 6 = 38

Number of females
= 3 u
= 3 x 38
= 114

(b)
Number of males
= 8 p
= 8 x 6
= 48

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

Number of males who do not wear glasses
= 8 p - 1 p
= 7 p

Number of people who do not wear glasses
= 162 - 44
= 118

Answer(s): (a) 114; (b) 48; (c) 118