180 children are in a school.
15 of the girls and
110 of the boys wear glasses.
22 children wear glasses.
- How many girls are there?
- How many boys are there?
- How many children do not wear glasses?
|
Number |
Girls |
Boys |
Total |
180 |
5 u |
10 p |
Wear glasses |
22 |
1 u |
1 p |
No glasses |
|
4 u |
9 p |
(a)
Number of girls = 5 u
Number of boys = 10 p
5 u + 10 p = 180 --- (1)
1 u + 1 p = 22 --- (2)
(2)
x 5 5 u + 5 p = 110 --- (3)
(1) - (3)
(5 u + 10 p) - (5 u + 5 p) = 180 - 110
5 u + 10 p - 5 u - 5 p = 70
5 p = 70
1 p = 70 ÷ 5 = 14
Substitute 1 p = 14 into (2).
1 u + 1 p = 22
1 u + 14 = 22
1 u = 22 - 14 = 8
Number of girls
= 5 u
= 5 x 8
= 40
(b)
Number of boys
= 10 p
= 10 x 14
= 140
(c)
Number of girls who do not wear glasses
= 5 u - 1 u
= 4 u
Number of boys who do not wear glasses
= 10 p - 1 p
= 9 p
Number of children who do not wear glasses
= 180 - 22
= 158
Answer(s): (a) 40; (b) 140; (c) 158