71 children are in a school.
13 of the boys and
110 of the girls wear glasses.
19 children wear glasses.
- How many boys are there?
- How many girls are there?
- How many children do not wear glasses?
|
Number |
Boys |
Girls |
Total |
71 |
3 u |
10 p |
Wear glasses |
19 |
1 u |
1 p |
No glasses |
|
2 u |
9 p |
(a)
Number of boys = 3 u
Number of girls = 10 p
3 u + 10 p = 71 --- (1)
1 u + 1 p = 19 --- (2)
(2)
x 3 3 u + 3 p = 57 --- (3)
(1) - (3)
(3 u + 10 p) - (3 u + 3 p) = 71 - 57
3 u + 10 p - 3 u - 3 p = 14
7 p = 14
1 p = 14 ÷ 7 = 2
Substitute 1 p = 2 into (2).
1 u + 1 p = 19
1 u + 2 = 19
1 u = 19 - 2 = 17
Number of boys
= 3 u
= 3 x 17
= 51
(b)
Number of girls
= 10 p
= 10 x 2
= 20
(c)
Number of boys who do not wear glasses
= 3 u - 1 u
= 2 u
Number of girls who do not wear glasses
= 10 p - 1 p
= 9 p
Number of children who do not wear glasses
= 71 - 19
= 52
Answer(s): (a) 51; (b) 20; (c) 52