267 children are in a school.
13 of the boys and
17 of the girls wear glasses.
41 children wear glasses.
- How many boys are there?
- How many girls are there?
- How many children do not wear glasses?
|
Number |
Boys |
Girls |
Total |
267 |
3 u |
7 p |
Wear glasses |
41 |
1 u |
1 p |
No glasses |
|
2 u |
6 p |
(a)
Number of boys = 3 u
Number of girls = 7 p
3 u + 7 p = 267 --- (1)
1 u + 1 p = 41 --- (2)
(2)
x 3 3 u + 3 p = 123 --- (3)
(1) - (3)
(3 u + 7 p) - (3 u + 3 p) = 267 - 123
3 u + 7 p - 3 u - 3 p = 144
4 p = 144
1 p = 144 ÷ 4 = 36
Substitute 1 p = 36 into (2).
1 u + 1 p = 41
1 u + 36 = 41
1 u = 41 - 36 = 5
Number of boys
= 3 u
= 3 x 5
= 15
(b)
Number of girls
= 7 p
= 7 x 36
= 252
(c)
Number of boys who do not wear glasses
= 3 u - 1 u
= 2 u
Number of girls who do not wear glasses
= 7 p - 1 p
= 6 p
Number of children who do not wear glasses
= 267 - 41
= 226
Answer(s): (a) 15; (b) 252; (c) 226