220 children are in a school.
14 of the boys and
17 of the girls wear glasses.
34 children wear glasses.
- How many boys are there?
- How many girls are there?
- How many children do not wear glasses?
|
Number |
Boys |
Girls |
Total |
220 |
4 u |
7 p |
Wear glasses |
34 |
1 u |
1 p |
No glasses |
|
3 u |
6 p |
(a)
Number of boys = 4 u
Number of girls = 7 p
4 u + 7 p = 220 --- (1)
1 u + 1 p = 34 --- (2)
(2)
x 4 4 u + 4 p = 136 --- (3)
(1) - (3)
(4 u + 7 p) - (4 u + 4 p) = 220 - 136
4 u + 7 p - 4 u - 4 p = 84
3 p = 84
1 p = 84 ÷ 3 = 28
Substitute 1 p = 28 into (2).
1 u + 1 p = 34
1 u + 28 = 34
1 u = 34 - 28 = 6
Number of boys
= 4 u
= 4 x 6
= 24
(b)
Number of girls
= 7 p
= 7 x 28
= 196
(c)
Number of boys who do not wear glasses
= 4 u - 1 u
= 3 u
Number of girls who do not wear glasses
= 7 p - 1 p
= 6 p
Number of children who do not wear glasses
= 220 - 34
= 186
Answer(s): (a) 24; (b) 196; (c) 186