265 people are in a school.
¹₃ of the females and
¹₇ of the males wear glasses.
47 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	265	3 u	7 p
Wear glasses	47	1 u	1 p
No glasses		2 u	6 p

(a)
Number of females = 3 u
Number of males = 7 p

3 u + 7 p = 265 --- (1)
1 u + 1 p = 47 --- (2)

(2) _{x 3}
3 u + 3 p = 141 --- (3)

(1) - (3)
(3 u + 7 p) - (3 u + 3 p) = 265 - 141
3 u + 7 p - 3 u - 3 p = 124
4 p = 124

1 p = 124 ÷ 4 = 31

Substitute 1 p = 31 into (2).

1 u + 1 p = 47
1 u + 31 = 47

1 u = 47 - 31 = 16

Number of females
= 3 u
= 3 x 16
= 48

(b)
Number of males
= 7 p
= 7 x 31
= 217

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

Number of males who do not wear glasses
= 7 p - 1 p
= 6 p

Number of people who do not wear glasses
= 265 - 47
= 218

Answer(s): (a) 48; (b) 217; (c) 218