193 children are in a school.
¹₄ of the boys and
¹₉ of the girls wear glasses.
32 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	193	4 u	9 p
Wear glasses	32	1 u	1 p
No glasses		3 u	8 p

(a)
Number of boys = 4 u
Number of girls = 9 p

4 u + 9 p = 193 --- (1)
1 u + 1 p = 32 --- (2)

(2) _{x 4}
4 u + 4 p = 128 --- (3)

(1) - (3)
(4 u + 9 p) - (4 u + 4 p) = 193 - 128
4 u + 9 p - 4 u - 4 p = 65
5 p = 65

1 p = 65 ÷ 5 = 13

Substitute 1 p = 13 into (2).

1 u + 1 p = 32
1 u + 13 = 32

1 u = 32 - 13 = 19

Number of boys
= 4 u
= 4 x 19
= 76

(b)
Number of girls
= 9 p
= 9 x 13
= 117

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

Number of girls who do not wear glasses
= 9 p - 1 p
= 8 p

Number of children who do not wear glasses
= 193 - 32
= 161

Answer(s): (a) 76; (b) 117; (c) 161