81 adults are in a school.
13 of the women and
15 of the men wear glasses.
23 adults wear glasses.
- How many women are there?
- How many men are there?
- How many adults do not wear glasses?
|
Number |
Women |
Men |
Total |
81 |
3 u |
5 p |
Wear glasses |
23 |
1 u |
1 p |
No glasses |
|
2 u |
4 p |
(a)
Number of women = 3 u
Number of men = 5 p
3 u + 5 p = 81 --- (1)
1 u + 1 p = 23 --- (2)
(2)
x 3 3 u + 3 p = 69 --- (3)
(1) - (3)
(3 u + 5 p) - (3 u + 3 p) = 81 - 69
3 u + 5 p - 3 u - 3 p = 12
2 p = 12
1 p = 12 ÷ 2 = 6
Substitute 1 p = 6 into (2).
1 u + 1 p = 23
1 u + 6 = 23
1 u = 23 - 6 = 17
Number of women
= 3 u
= 3 x 17
= 51
(b)
Number of men
= 5 p
= 5 x 6
= 30
(c)
Number of women who do not wear glasses
= 3 u - 1 u
= 2 u
Number of men who do not wear glasses
= 5 p - 1 p
= 4 p
Number of adults who do not wear glasses
= 81 - 23
= 58
Answer(s): (a) 51; (b) 30; (c) 58