242 children are in a school.
14 of the girls and
110 of the boys wear glasses.
50 children wear glasses.
- How many girls are there?
- How many boys are there?
- How many children do not wear glasses?
|
Number |
Girls |
Boys |
Total |
242 |
4 u |
10 p |
Wear glasses |
50 |
1 u |
1 p |
No glasses |
|
3 u |
9 p |
(a)
Number of girls = 4 u
Number of boys = 10 p
4 u + 10 p = 242 --- (1)
1 u + 1 p = 50 --- (2)
(2)
x 4 4 u + 4 p = 200 --- (3)
(1) - (3)
(4 u + 10 p) - (4 u + 4 p) = 242 - 200
4 u + 10 p - 4 u - 4 p = 42
6 p = 42
1 p = 42 ÷ 6 = 7
Substitute 1 p = 7 into (2).
1 u + 1 p = 50
1 u + 7 = 50
1 u = 50 - 7 = 43
Number of girls
= 4 u
= 4 x 43
= 172
(b)
Number of boys
= 10 p
= 10 x 7
= 70
(c)
Number of girls who do not wear glasses
= 4 u - 1 u
= 3 u
Number of boys who do not wear glasses
= 10 p - 1 p
= 9 p
Number of children who do not wear glasses
= 242 - 50
= 192
Answer(s): (a) 172; (b) 70; (c) 192