175 children are in a school.
15 of the boys and
110 of the girls wear glasses.
24 children wear glasses.
- How many boys are there?
- How many girls are there?
- How many children do not wear glasses?
|
Number |
Boys |
Girls |
Total |
175 |
5 u |
10 p |
Wear glasses |
24 |
1 u |
1 p |
No glasses |
|
4 u |
9 p |
(a)
Number of boys = 5 u
Number of girls = 10 p
5 u + 10 p = 175 --- (1)
1 u + 1 p = 24 --- (2)
(2)
x 5 5 u + 5 p = 120 --- (3)
(1) - (3)
(5 u + 10 p) - (5 u + 5 p) = 175 - 120
5 u + 10 p - 5 u - 5 p = 55
5 p = 55
1 p = 55 ÷ 5 = 11
Substitute 1 p = 11 into (2).
1 u + 1 p = 24
1 u + 11 = 24
1 u = 24 - 11 = 13
Number of boys
= 5 u
= 5 x 13
= 65
(b)
Number of girls
= 10 p
= 10 x 11
= 110
(c)
Number of boys who do not wear glasses
= 5 u - 1 u
= 4 u
Number of girls who do not wear glasses
= 10 p - 1 p
= 9 p
Number of children who do not wear glasses
= 175 - 24
= 151
Answer(s): (a) 65; (b) 110; (c) 151