262 children are in a school.
14 of the boys and
16 of the girls wear glasses.
46 children wear glasses.
- How many boys are there?
- How many girls are there?
- How many children do not wear glasses?
|
Number |
Boys |
Girls |
Total |
262 |
4 u |
6 p |
Wear glasses |
46 |
1 u |
1 p |
No glasses |
|
3 u |
5 p |
(a)
Number of boys = 4 u
Number of girls = 6 p
4 u + 6 p = 262 --- (1)
1 u + 1 p = 46 --- (2)
(2)
x 4 4 u + 4 p = 184 --- (3)
(1) - (3)
(4 u + 6 p) - (4 u + 4 p) = 262 - 184
4 u + 6 p - 4 u - 4 p = 78
2 p = 78
1 p = 78 ÷ 2 = 39
Substitute 1 p = 39 into (2).
1 u + 1 p = 46
1 u + 39 = 46
1 u = 46 - 39 = 7
Number of boys
= 4 u
= 4 x 7
= 28
(b)
Number of girls
= 6 p
= 6 x 39
= 234
(c)
Number of boys who do not wear glasses
= 4 u - 1 u
= 3 u
Number of girls who do not wear glasses
= 6 p - 1 p
= 5 p
Number of children who do not wear glasses
= 262 - 46
= 216
Answer(s): (a) 28; (b) 234; (c) 216