133 children are in a school.
¹₄ of the girls and
¹₉ of the boys wear glasses.
27 children wear glasses.

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

	Number	Girls	Boys
Total	133	4 u	9 p
Wear glasses	27	1 u	1 p
No glasses		3 u	8 p

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

4 u + 9 p = 133 --- (1)
1 u + 1 p = 27 --- (2)

(2) _{x 4}
4 u + 4 p = 108 --- (3)

(1) - (3)
(4 u + 9 p) - (4 u + 4 p) = 133 - 108
4 u + 9 p - 4 u - 4 p = 25
5 p = 25

1 p = 25 ÷ 5 = 5

Substitute 1 p = 5 into (2).

1 u + 1 p = 27
1 u + 5 = 27

1 u = 27 - 5 = 22

Number of girls
= 4 u
= 4 x 22
= 88

(b)
Number of boys
= 9 p
= 9 x 5
= 45

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

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

Number of children who do not wear glasses
= 133 - 27
= 106

Answer(s): (a) 88; (b) 45; (c) 106