254 children are in a school.
¹₄ of the girls and
¹₆ of the boys wear glasses.
45 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	254	4 u	6 p
Wear glasses	45	1 u	1 p
No glasses		3 u	5 p

(a)
Number of girls = 4 u
Number of boys = 6 p

4 u + 6 p = 254 --- (1)
1 u + 1 p = 45 --- (2)

(2) _{x 4}
4 u + 4 p = 180 --- (3)

(1) - (3)
(4 u + 6 p) - (4 u + 4 p) = 254 - 180
4 u + 6 p - 4 u - 4 p = 74
2 p = 74

1 p = 74 ÷ 2 = 37

Substitute 1 p = 37 into (2).

1 u + 1 p = 45
1 u + 37 = 45

1 u = 45 - 37 = 8

Number of girls
= 4 u
= 4 x 8
= 32

(b)
Number of boys
= 6 p
= 6 x 37
= 222

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

Number of boys who do not wear glasses
= 6 p - 1 p
= 5 p

Number of children who do not wear glasses
= 254 - 45
= 209

Answer(s): (a) 32; (b) 222; (c) 209