201 children are in a school.
15 of the boys and
17 of the girls wear glasses.
37 children wear glasses.
- How many boys are there?
- How many girls are there?
- How many children do not wear glasses?
|
Number |
Boys |
Girls |
Total |
201 |
5 u |
7 p |
Wear glasses |
37 |
1 u |
1 p |
No glasses |
|
4 u |
6 p |
(a)
Number of boys = 5 u
Number of girls = 7 p
5 u + 7 p = 201 --- (1)
1 u + 1 p = 37 --- (2)
(2)
x 5 5 u + 5 p = 185 --- (3)
(1) - (3)
(5 u + 7 p) - (5 u + 5 p) = 201 - 185
5 u + 7 p - 5 u - 5 p = 16
2 p = 16
1 p = 16 ÷ 2 = 8
Substitute 1 p = 8 into (2).
1 u + 1 p = 37
1 u + 8 = 37
1 u = 37 - 8 = 29
Number of boys
= 5 u
= 5 x 29
= 145
(b)
Number of girls
= 7 p
= 7 x 8
= 56
(c)
Number of boys who do not wear glasses
= 5 u - 1 u
= 4 u
Number of girls who do not wear glasses
= 7 p - 1 p
= 6 p
Number of children who do not wear glasses
= 201 - 37
= 164
Answer(s): (a) 145; (b) 56; (c) 164