162 adults are in a school.
13 of the men and
16 of the women wear glasses.
44 adults wear glasses.
- How many men are there?
- How many women are there?
- How many adults do not wear glasses?
|
Number |
Men |
Women |
Total |
162 |
3 u |
6 p |
Wear glasses |
44 |
1 u |
1 p |
No glasses |
|
2 u |
5 p |
(a)
Number of men = 3 u
Number of women = 6 p
3 u + 6 p = 162 --- (1)
1 u + 1 p = 44 --- (2)
(2)
x 3 3 u + 3 p = 132 --- (3)
(1) - (3)
(3 u + 6 p) - (3 u + 3 p) = 162 - 132
3 u + 6 p - 3 u - 3 p = 30
3 p = 30
1 p = 30 ÷ 3 = 10
Substitute 1 p = 10 into (2).
1 u + 1 p = 44
1 u + 10 = 44
1 u = 44 - 10 = 34
Number of men
= 3 u
= 3 x 34
= 102
(b)
Number of women
= 6 p
= 6 x 10
= 60
(c)
Number of men who do not wear glasses
= 3 u - 1 u
= 2 u
Number of women who do not wear glasses
= 6 p - 1 p
= 5 p
Number of adults who do not wear glasses
= 162 - 44
= 118
Answer(s): (a) 102; (b) 60; (c) 118