243 children are in a school.
14 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 |
243 |
4 u |
9 p |
Wear glasses |
47 |
1 u |
1 p |
No glasses |
|
3 u |
8 p |
(a)
Number of girls = 4 u
Number of boys = 9 p
4 u + 9 p = 243 --- (1)
1 u + 1 p = 47 --- (2)
(2)
x 4 4 u + 4 p = 188 --- (3)
(1) - (3)
(4 u + 9 p) - (4 u + 4 p) = 243 - 188
4 u + 9 p - 4 u - 4 p = 55
5 p = 55
1 p = 55 ÷ 5 = 11
Substitute 1 p = 11 into (2).
1 u + 1 p = 47
1 u + 11 = 47
1 u = 47 - 11 = 36
Number of girls
= 4 u
= 4 x 36
= 144
(b)
Number of boys
= 9 p
= 9 x 11
= 99
(c)
Number of girls who do not wear glasses
= 4 u - 1 u
= 3 u
Number of boys who do not wear glasses
= 9 p - 1 p
= 8 p
Number of children who do not wear glasses
= 243 - 47
= 196
Answer(s): (a) 144; (b) 99; (c) 196