64 children are in a school.
14 of the girls and
18 of the boys wear glasses.
10 children wear glasses.
- How many girls are there?
- How many boys are there?
- How many children do not wear glasses?
|
Number |
Girls |
Boys |
Total |
64 |
4 u |
8 p |
Wear glasses |
10 |
1 u |
1 p |
No glasses |
|
3 u |
7 p |
(a)
Number of girls = 4 u
Number of boys = 8 p
4 u + 8 p = 64 --- (1)
1 u + 1 p = 10 --- (2)
(2)
x 4 4 u + 4 p = 40 --- (3)
(1) - (3)
(4 u + 8 p) - (4 u + 4 p) = 64 - 40
4 u + 8 p - 4 u - 4 p = 24
4 p = 24
1 p = 24 ÷ 4 = 6
Substitute 1 p = 6 into (2).
1 u + 1 p = 10
1 u + 6 = 10
1 u = 10 - 6 = 4
Number of girls
= 4 u
= 4 x 4
= 16
(b)
Number of boys
= 8 p
= 8 x 6
= 48
(c)
Number of girls who do not wear glasses
= 4 u - 1 u
= 3 u
Number of boys who do not wear glasses
= 8 p - 1 p
= 7 p
Number of children who do not wear glasses
= 64 - 10
= 54
Answer(s): (a) 16; (b) 48; (c) 54