192 children are in a school.
15 of the girls and
17 of the boys wear glasses.
32 children wear glasses.
- How many girls are there?
- How many boys are there?
- How many children do not wear glasses?
|
Number |
Girls |
Boys |
Total |
192 |
5 u |
7 p |
Wear glasses |
32 |
1 u |
1 p |
No glasses |
|
4 u |
6 p |
(a)
Number of girls = 5 u
Number of boys = 7 p
5 u + 7 p = 192 --- (1)
1 u + 1 p = 32 --- (2)
(2)
x 5 5 u + 5 p = 160 --- (3)
(1) - (3)
(5 u + 7 p) - (5 u + 5 p) = 192 - 160
5 u + 7 p - 5 u - 5 p = 32
2 p = 32
1 p = 32 ÷ 2 = 16
Substitute 1 p = 16 into (2).
1 u + 1 p = 32
1 u + 16 = 32
1 u = 32 - 16 = 16
Number of girls
= 5 u
= 5 x 16
= 80
(b)
Number of boys
= 7 p
= 7 x 16
= 112
(c)
Number of girls who do not wear glasses
= 5 u - 1 u
= 4 u
Number of boys who do not wear glasses
= 7 p - 1 p
= 6 p
Number of children who do not wear glasses
= 192 - 32
= 160
Answer(s): (a) 80; (b) 112; (c) 160