177 adults are in a school.
13 of the men and
16 of the women wear glasses.
41 adults wear glasses.
- How many men are there?
- How many women are there?
- How many adults do not wear glasses?
|
Number |
Men |
Women |
Total |
177 |
3 u |
6 p |
Wear glasses |
41 |
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 = 177 --- (1)
1 u + 1 p = 41 --- (2)
(2)
x 3 3 u + 3 p = 123 --- (3)
(1) - (3)
(3 u + 6 p) - (3 u + 3 p) = 177 - 123
3 u + 6 p - 3 u - 3 p = 54
3 p = 54
1 p = 54 ÷ 3 = 18
Substitute 1 p = 18 into (2).
1 u + 1 p = 41
1 u + 18 = 41
1 u = 41 - 18 = 23
Number of men
= 3 u
= 3 x 23
= 69
(b)
Number of women
= 6 p
= 6 x 18
= 108
(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
= 177 - 41
= 136
Answer(s): (a) 69; (b) 108; (c) 136