233 children are in a school.
13 of the boys and
17 of the girls wear glasses.
47 children wear glasses.
- How many boys are there?
- How many girls are there?
- How many children do not wear glasses?
|
Number |
Boys |
Girls |
Total |
233 |
3 u |
7 p |
Wear glasses |
47 |
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 = 233 --- (1)
1 u + 1 p = 47 --- (2)
(2)
x 3 3 u + 3 p = 141 --- (3)
(1) - (3)
(3 u + 7 p) - (3 u + 3 p) = 233 - 141
3 u + 7 p - 3 u - 3 p = 92
4 p = 92
1 p = 92 ÷ 4 = 23
Substitute 1 p = 23 into (2).
1 u + 1 p = 47
1 u + 23 = 47
1 u = 47 - 23 = 24
Number of boys
= 3 u
= 3 x 24
= 72
(b)
Number of girls
= 7 p
= 7 x 23
= 161
(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
= 233 - 47
= 186
Answer(s): (a) 72; (b) 161; (c) 186