177 children are in a school.
13 of the girls and
15 of the boys wear glasses.
37 children wear glasses.
- How many girls are there?
- How many boys are there?
- How many children do not wear glasses?
|
Number |
Girls |
Boys |
Total |
177 |
3 u |
5 p |
Wear glasses |
37 |
1 u |
1 p |
No glasses |
|
2 u |
4 p |
(a)
Number of girls = 3 u
Number of boys = 5 p
3 u + 5 p = 177 --- (1)
1 u + 1 p = 37 --- (2)
(2)
x 3 3 u + 3 p = 111 --- (3)
(1) - (3)
(3 u + 5 p) - (3 u + 3 p) = 177 - 111
3 u + 5 p - 3 u - 3 p = 66
2 p = 66
1 p = 66 ÷ 2 = 33
Substitute 1 p = 33 into (2).
1 u + 1 p = 37
1 u + 33 = 37
1 u = 37 - 33 = 4
Number of girls
= 3 u
= 3 x 4
= 12
(b)
Number of boys
= 5 p
= 5 x 33
= 165
(c)
Number of girls who do not wear glasses
= 3 u - 1 u
= 2 u
Number of boys who do not wear glasses
= 5 p - 1 p
= 4 p
Number of children who do not wear glasses
= 177 - 37
= 140
Answer(s): (a) 12; (b) 165; (c) 140