213 children are in a school.
13 of the boys and
18 of the girls wear glasses.
31 children wear glasses.
- How many boys are there?
- How many girls are there?
- How many children do not wear glasses?
|
Number |
Boys |
Girls |
Total |
213 |
3 u |
8 p |
Wear glasses |
31 |
1 u |
1 p |
No glasses |
|
2 u |
7 p |
(a)
Number of boys = 3 u
Number of girls = 8 p
3 u + 8 p = 213 --- (1)
1 u + 1 p = 31 --- (2)
(2)
x 3 3 u + 3 p = 93 --- (3)
(1) - (3)
(3 u + 8 p) - (3 u + 3 p) = 213 - 93
3 u + 8 p - 3 u - 3 p = 120
5 p = 120
1 p = 120 ÷ 5 = 24
Substitute 1 p = 24 into (2).
1 u + 1 p = 31
1 u + 24 = 31
1 u = 31 - 24 = 7
Number of boys
= 3 u
= 3 x 7
= 21
(b)
Number of girls
= 8 p
= 8 x 24
= 192
(c)
Number of boys who do not wear glasses
= 3 u - 1 u
= 2 u
Number of girls who do not wear glasses
= 8 p - 1 p
= 7 p
Number of children who do not wear glasses
= 213 - 31
= 182
Answer(s): (a) 21; (b) 192; (c) 182