96 adults are in a school.
14 of the women and
16 of the men wear glasses.
22 adults wear glasses.
- How many women are there?
- How many men are there?
- How many adults do not wear glasses?
|
Number |
Women |
Men |
Total |
96 |
4 u |
6 p |
Wear glasses |
22 |
1 u |
1 p |
No glasses |
|
3 u |
5 p |
(a)
Number of women = 4 u
Number of men = 6 p
4 u + 6 p = 96 --- (1)
1 u + 1 p = 22 --- (2)
(2)
x 4 4 u + 4 p = 88 --- (3)
(1) - (3)
(4 u + 6 p) - (4 u + 4 p) = 96 - 88
4 u + 6 p - 4 u - 4 p = 8
2 p = 8
1 p = 8 ÷ 2 = 4
Substitute 1 p = 4 into (2).
1 u + 1 p = 22
1 u + 4 = 22
1 u = 22 - 4 = 18
Number of women
= 4 u
= 4 x 18
= 72
(b)
Number of men
= 6 p
= 6 x 4
= 24
(c)
Number of women who do not wear glasses
= 4 u - 1 u
= 3 u
Number of men who do not wear glasses
= 6 p - 1 p
= 5 p
Number of adults who do not wear glasses
= 96 - 22
= 74
Answer(s): (a) 72; (b) 24; (c) 74