162 children are in a school.
13 of the boys and
16 of the girls wear glasses.
36 children wear glasses.
- How many boys are there?
- How many girls are there?
- How many children do not wear glasses?
|
Number |
Boys |
Girls |
Total |
162 |
3 u |
6 p |
Wear glasses |
36 |
1 u |
1 p |
No glasses |
|
2 u |
5 p |
(a)
Number of boys = 3 u
Number of girls = 6 p
3 u + 6 p = 162 --- (1)
1 u + 1 p = 36 --- (2)
(2)
x 3 3 u + 3 p = 108 --- (3)
(1) - (3)
(3 u + 6 p) - (3 u + 3 p) = 162 - 108
3 u + 6 p - 3 u - 3 p = 54
3 p = 54
1 p = 54 ÷ 3 = 18
Substitute 1 p = 18 into (2).
1 u + 1 p = 36
1 u + 18 = 36
1 u = 36 - 18 = 18
Number of boys
= 3 u
= 3 x 18
= 54
(b)
Number of girls
= 6 p
= 6 x 18
= 108
(c)
Number of boys who do not wear glasses
= 3 u - 1 u
= 2 u
Number of girls who do not wear glasses
= 6 p - 1 p
= 5 p
Number of children who do not wear glasses
= 162 - 36
= 126
Answer(s): (a) 54; (b) 108; (c) 126