117 children are in a school.
13 of the girls and
19 of the boys wear glasses.
17 children wear glasses.
- How many girls are there?
- How many boys are there?
- How many children do not wear glasses?
|
Number |
Girls |
Boys |
Total |
117 |
3 u |
9 p |
Wear glasses |
17 |
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 = 117 --- (1)
1 u + 1 p = 17 --- (2)
(2)
x 3 3 u + 3 p = 51 --- (3)
(1) - (3)
(3 u + 9 p) - (3 u + 3 p) = 117 - 51
3 u + 9 p - 3 u - 3 p = 66
6 p = 66
1 p = 66 ÷ 6 = 11
Substitute 1 p = 11 into (2).
1 u + 1 p = 17
1 u + 11 = 17
1 u = 17 - 11 = 6
Number of girls
= 3 u
= 3 x 6
= 18
(b)
Number of boys
= 9 p
= 9 x 11
= 99
(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
= 117 - 17
= 100
Answer(s): (a) 18; (b) 99; (c) 100