164 children are in a school.
14 of the boys and
110 of the girls wear glasses.
20 children wear glasses.
- How many boys are there?
- How many girls are there?
- How many children do not wear glasses?
|
Number |
Boys |
Girls |
Total |
164 |
4 u |
10 p |
Wear glasses |
20 |
1 u |
1 p |
No glasses |
|
3 u |
9 p |
(a)
Number of boys = 4 u
Number of girls = 10 p
4 u + 10 p = 164 --- (1)
1 u + 1 p = 20 --- (2)
(2)
x 4 4 u + 4 p = 80 --- (3)
(1) - (3)
(4 u + 10 p) - (4 u + 4 p) = 164 - 80
4 u + 10 p - 4 u - 4 p = 84
6 p = 84
1 p = 84 ÷ 6 = 14
Substitute 1 p = 14 into (2).
1 u + 1 p = 20
1 u + 14 = 20
1 u = 20 - 14 = 6
Number of boys
= 4 u
= 4 x 6
= 24
(b)
Number of girls
= 10 p
= 10 x 14
= 140
(c)
Number of boys who do not wear glasses
= 4 u - 1 u
= 3 u
Number of girls who do not wear glasses
= 10 p - 1 p
= 9 p
Number of children who do not wear glasses
= 164 - 20
= 144
Answer(s): (a) 24; (b) 140; (c) 144