147 children are in a school.
13 of the girls and
19 of the boys wear glasses.
47 children wear glasses.
- How many girls are there?
- How many boys are there?
- How many children do not wear glasses?
|
Number |
Girls |
Boys |
Total |
147 |
3 u |
9 p |
Wear glasses |
47 |
1 u |
1 p |
No glasses |
|
2 u |
8 p |
(a)
Number of girls = 3 u
Number of boys = 9 p
3 u + 9 p = 147 --- (1)
1 u + 1 p = 47 --- (2)
(2)
x 3 3 u + 3 p = 141 --- (3)
(1) - (3)
(3 u + 9 p) - (3 u + 3 p) = 147 - 141
3 u + 9 p - 3 u - 3 p = 6
6 p = 6
1 p = 6 ÷ 6 = 1
Substitute 1 p = 1 into (2).
1 u + 1 p = 47
1 u + 1 = 47
1 u = 47 - 1 = 46
Number of girls
= 3 u
= 3 x 46
= 138
(b)
Number of boys
= 9 p
= 9 x 1
= 9
(c)
Number of girls who do not wear glasses
= 3 u - 1 u
= 2 u
Number of boys who do not wear glasses
= 9 p - 1 p
= 8 p
Number of children who do not wear glasses
= 147 - 47
= 100
Answer(s): (a) 138; (b) 9; (c) 100