222 adults are in a school.
¹₃ of the women and
¹₈ of the men wear glasses.
49 adults wear glasses.

1. How many women are there?
2. How many men are there?
3. How many adults do not wear glasses?

	Number	Women	Men
Total	222	3 u	8 p
Wear glasses	49	1 u	1 p
No glasses		2 u	7 p

(a)
Number of women = 3 u
Number of men = 8 p

3 u + 8 p = 222 --- (1)
1 u + 1 p = 49 --- (2)

(2) _{x 3}
3 u + 3 p = 147 --- (3)

(1) - (3)
(3 u + 8 p) - (3 u + 3 p) = 222 - 147
3 u + 8 p - 3 u - 3 p = 75
5 p = 75

1 p = 75 ÷ 5 = 15

Substitute 1 p = 15 into (2).

1 u + 1 p = 49
1 u + 15 = 49

1 u = 49 - 15 = 34

Number of women
= 3 u
= 3 x 34
= 102

(b)
Number of men
= 8 p
= 8 x 15
= 120

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

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

Number of adults who do not wear glasses
= 222 - 49
= 173

Answer(s): (a) 102; (b) 120; (c) 173