177 children are in a school.
15 of the girls and
18 of the boys wear glasses.
33 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 |
5 u |
8 p |
Wear glasses |
33 |
1 u |
1 p |
No glasses |
|
4 u |
7 p |
(a)
Number of girls = 5 u
Number of boys = 8 p
5 u + 8 p = 177 --- (1)
1 u + 1 p = 33 --- (2)
(2)
x 5 5 u + 5 p = 165 --- (3)
(1) - (3)
(5 u + 8 p) - (5 u + 5 p) = 177 - 165
5 u + 8 p - 5 u - 5 p = 12
3 p = 12
1 p = 12 ÷ 3 = 4
Substitute 1 p = 4 into (2).
1 u + 1 p = 33
1 u + 4 = 33
1 u = 33 - 4 = 29
Number of girls
= 5 u
= 5 x 29
= 145
(b)
Number of boys
= 8 p
= 8 x 4
= 32
(c)
Number of girls who do not wear glasses
= 5 u - 1 u
= 4 u
Number of boys who do not wear glasses
= 8 p - 1 p
= 7 p
Number of children who do not wear glasses
= 177 - 33
= 144
Answer(s): (a) 145; (b) 32; (c) 144