269 children are in a school.
14 of the girls and
19 of the boys wear glasses.
31 children wear glasses.
- How many girls are there?
- How many boys are there?
- How many children do not wear glasses?
|
Number |
Girls |
Boys |
Total |
269 |
4 u |
9 p |
Wear glasses |
31 |
1 u |
1 p |
No glasses |
|
3 u |
8 p |
(a)
Number of girls = 4 u
Number of boys = 9 p
4 u + 9 p = 269 --- (1)
1 u + 1 p = 31 --- (2)
(2)
x 4 4 u + 4 p = 124 --- (3)
(1) - (3)
(4 u + 9 p) - (4 u + 4 p) = 269 - 124
4 u + 9 p - 4 u - 4 p = 145
5 p = 145
1 p = 145 ÷ 5 = 29
Substitute 1 p = 29 into (2).
1 u + 1 p = 31
1 u + 29 = 31
1 u = 31 - 29 = 2
Number of girls
= 4 u
= 4 x 2
= 8
(b)
Number of boys
= 9 p
= 9 x 29
= 261
(c)
Number of girls who do not wear glasses
= 4 u - 1 u
= 3 u
Number of boys who do not wear glasses
= 9 p - 1 p
= 8 p
Number of children who do not wear glasses
= 269 - 31
= 238
Answer(s): (a) 8; (b) 261; (c) 238