169 children are in a school.
¹₅ of the boys and
¹₈ of the girls wear glasses.
29 children wear glasses.

1. How many boys are there?
2. How many girls are there?
3. How many children do not wear glasses?

	Number	Boys	Girls
Total	169	5 u	8 p
Wear glasses	29	1 u	1 p
No glasses		4 u	7 p

(a)
Number of boys = 5 u
Number of girls = 8 p

5 u + 8 p = 169 --- (1)
1 u + 1 p = 29 --- (2)

(2) _{x 5}
5 u + 5 p = 145 --- (3)

(1) - (3)
(5 u + 8 p) - (5 u + 5 p) = 169 - 145
5 u + 8 p - 5 u - 5 p = 24
3 p = 24

1 p = 24 ÷ 3 = 8

Substitute 1 p = 8 into (2).

1 u + 1 p = 29
1 u + 8 = 29

1 u = 29 - 8 = 21

Number of boys
= 5 u
= 5 x 21
= 105

(b)
Number of girls
= 8 p
= 8 x 8
= 64

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

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

Number of children who do not wear glasses
= 169 - 29
= 140

Answer(s): (a) 105; (b) 64; (c) 140