169 children are in a school.
13 of the boys and
15 of the girls wear glasses.
43 children wear glasses.
- How many boys are there?
- How many girls are there?
- How many children do not wear glasses?
|
Number |
Boys |
Girls |
Total |
169 |
3 u |
5 p |
Wear glasses |
43 |
1 u |
1 p |
No glasses |
|
2 u |
4 p |
(a)
Number of boys = 3 u
Number of girls = 5 p
3 u + 5 p = 169 --- (1)
1 u + 1 p = 43 --- (2)
(2)
x 3 3 u + 3 p = 129 --- (3)
(1) - (3)
(3 u + 5 p) - (3 u + 3 p) = 169 - 129
3 u + 5 p - 3 u - 3 p = 40
2 p = 40
1 p = 40 ÷ 2 = 20
Substitute 1 p = 20 into (2).
1 u + 1 p = 43
1 u + 20 = 43
1 u = 43 - 20 = 23
Number of boys
= 3 u
= 3 x 23
= 69
(b)
Number of girls
= 5 p
= 5 x 20
= 100
(c)
Number of boys who do not wear glasses
= 3 u - 1 u
= 2 u
Number of girls who do not wear glasses
= 5 p - 1 p
= 4 p
Number of children who do not wear glasses
= 169 - 43
= 126
Answer(s): (a) 69; (b) 100; (c) 126