204 children are in a school.
13 of the girls and
18 of the boys wear glasses.
38 children wear glasses.
- How many girls are there?
- How many boys are there?
- How many children do not wear glasses?
|
Number |
Girls |
Boys |
Total |
204 |
3 u |
8 p |
Wear glasses |
38 |
1 u |
1 p |
No glasses |
|
2 u |
7 p |
(a)
Number of girls = 3 u
Number of boys = 8 p
3 u + 8 p = 204 --- (1)
1 u + 1 p = 38 --- (2)
(2)
x 3 3 u + 3 p = 114 --- (3)
(1) - (3)
(3 u + 8 p) - (3 u + 3 p) = 204 - 114
3 u + 8 p - 3 u - 3 p = 90
5 p = 90
1 p = 90 ÷ 5 = 18
Substitute 1 p = 18 into (2).
1 u + 1 p = 38
1 u + 18 = 38
1 u = 38 - 18 = 20
Number of girls
= 3 u
= 3 x 20
= 60
(b)
Number of boys
= 8 p
= 8 x 18
= 144
(c)
Number of girls who do not wear glasses
= 3 u - 1 u
= 2 u
Number of boys who do not wear glasses
= 8 p - 1 p
= 7 p
Number of children who do not wear glasses
= 204 - 38
= 166
Answer(s): (a) 60; (b) 144; (c) 166