290 people are in a school.
¹₅ of the females and
¹₁₀ of the males wear glasses.
33 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	290	5 u	10 p
Wear glasses	33	1 u	1 p
No glasses		4 u	9 p

(a)
Number of females = 5 u
Number of males = 10 p

5 u + 10 p = 290 --- (1)
1 u + 1 p = 33 --- (2)

(2) _{x 5}
5 u + 5 p = 165 --- (3)

(1) - (3)
(5 u + 10 p) - (5 u + 5 p) = 290 - 165
5 u + 10 p - 5 u - 5 p = 125
5 p = 125

1 p = 125 ÷ 5 = 25

Substitute 1 p = 25 into (2).

1 u + 1 p = 33
1 u + 25 = 33

1 u = 33 - 25 = 8

Number of females
= 5 u
= 5 x 8
= 40

(b)
Number of males
= 10 p
= 10 x 25
= 250

(c)
Number of females who do not wear glasses
= 5 u - 1 u
= 4 u

Number of males who do not wear glasses
= 10 p - 1 p
= 9 p

Number of people who do not wear glasses
= 290 - 33
= 257

Answer(s): (a) 40; (b) 250; (c) 257