212 adults are in a school.
¹₃ of the women and
¹₅ of the men wear glasses.
48 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	212	3 u	5 p
Wear glasses	48	1 u	1 p
No glasses		2 u	4 p

(a)
Number of women = 3 u
Number of men = 5 p

3 u + 5 p = 212 --- (1)
1 u + 1 p = 48 --- (2)

(2) _{x 3}
3 u + 3 p = 144 --- (3)

(1) - (3)
(3 u + 5 p) - (3 u + 3 p) = 212 - 144
3 u + 5 p - 3 u - 3 p = 68
2 p = 68

1 p = 68 ÷ 2 = 34

Substitute 1 p = 34 into (2).

1 u + 1 p = 48
1 u + 34 = 48

1 u = 48 - 34 = 14

Number of women
= 3 u
= 3 x 14
= 42

(b)
Number of men
= 5 p
= 5 x 34
= 170

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

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

Number of adults who do not wear glasses
= 212 - 48
= 164

Answer(s): (a) 42; (b) 170; (c) 164