160 adults are in a school.
¹₄ of the men and
¹₇ of the women wear glasses.
34 adults wear glasses.

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

	Number	Men	Women
Total	160	4 u	7 p
Wear glasses	34	1 u	1 p
No glasses		3 u	6 p

(a)
Number of men = 4 u
Number of women = 7 p

4 u + 7 p = 160 --- (1)
1 u + 1 p = 34 --- (2)

(2) _{x 4}
4 u + 4 p = 136 --- (3)

(1) - (3)
(4 u + 7 p) - (4 u + 4 p) = 160 - 136
4 u + 7 p - 4 u - 4 p = 24
3 p = 24

1 p = 24 ÷ 3 = 8

Substitute 1 p = 8 into (2).

1 u + 1 p = 34
1 u + 8 = 34

1 u = 34 - 8 = 26

Number of men
= 4 u
= 4 x 26
= 104

(b)
Number of women
= 7 p
= 7 x 8
= 56

(c)
Number of men who do not wear glasses
= 4 u - 1 u
= 3 u

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

Number of adults who do not wear glasses
= 160 - 34
= 126

Answer(s): (a) 104; (b) 56; (c) 126