172 children are in a school.
14 of the boys and
18 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 |
172 |
4 u |
8 p |
Wear glasses |
36 |
1 u |
1 p |
No glasses |
|
3 u |
7 p |
(a)
Number of boys = 4 u
Number of girls = 8 p
4 u + 8 p = 172 --- (1)
1 u + 1 p = 36 --- (2)
(2)
x 4 4 u + 4 p = 144 --- (3)
(1) - (3)
(4 u + 8 p) - (4 u + 4 p) = 172 - 144
4 u + 8 p - 4 u - 4 p = 28
4 p = 28
1 p = 28 ÷ 4 = 7
Substitute 1 p = 7 into (2).
1 u + 1 p = 36
1 u + 7 = 36
1 u = 36 - 7 = 29
Number of boys
= 4 u
= 4 x 29
= 116
(b)
Number of girls
= 8 p
= 8 x 7
= 56
(c)
Number of boys who do not wear glasses
= 4 u - 1 u
= 3 u
Number of girls who do not wear glasses
= 8 p - 1 p
= 7 p
Number of children who do not wear glasses
= 172 - 36
= 136
Answer(s): (a) 116; (b) 56; (c) 136