117 children are in a school.
14 of the boys and
17 of the girls wear glasses.
21 children wear glasses.
- How many boys are there?
- How many girls are there?
- How many children do not wear glasses?
|
Number |
Boys |
Girls |
Total |
117 |
4 u |
7 p |
Wear glasses |
21 |
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 = 117 --- (1)
1 u + 1 p = 21 --- (2)
(2)
x 4 4 u + 4 p = 84 --- (3)
(1) - (3)
(4 u + 7 p) - (4 u + 4 p) = 117 - 84
4 u + 7 p - 4 u - 4 p = 33
3 p = 33
1 p = 33 ÷ 3 = 11
Substitute 1 p = 11 into (2).
1 u + 1 p = 21
1 u + 11 = 21
1 u = 21 - 11 = 10
Number of boys
= 4 u
= 4 x 10
= 40
(b)
Number of girls
= 7 p
= 7 x 11
= 77
(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
= 117 - 21
= 96
Answer(s): (a) 40; (b) 77; (c) 96