114 adults are in a school.
13 of the women and
16 of the men wear glasses.
33 adults wear glasses.
- How many women are there?
- How many men are there?
- How many adults do not wear glasses?
|
Number |
Women |
Men |
Total |
114 |
3 u |
6 p |
Wear glasses |
33 |
1 u |
1 p |
No glasses |
|
2 u |
5 p |
(a)
Number of women = 3 u
Number of men = 6 p
3 u + 6 p = 114 --- (1)
1 u + 1 p = 33 --- (2)
(2)
x 3 3 u + 3 p = 99 --- (3)
(1) - (3)
(3 u + 6 p) - (3 u + 3 p) = 114 - 99
3 u + 6 p - 3 u - 3 p = 15
3 p = 15
1 p = 15 ÷ 3 = 5
Substitute 1 p = 5 into (2).
1 u + 1 p = 33
1 u + 5 = 33
1 u = 33 - 5 = 28
Number of women
= 3 u
= 3 x 28
= 84
(b)
Number of men
= 6 p
= 6 x 5
= 30
(c)
Number of women who do not wear glasses
= 3 u - 1 u
= 2 u
Number of men who do not wear glasses
= 6 p - 1 p
= 5 p
Number of adults who do not wear glasses
= 114 - 33
= 81
Answer(s): (a) 84; (b) 30; (c) 81