174 adults are in a school.
14 of the men and
16 of the women wear glasses.
35 adults wear glasses.
- How many men are there?
- How many women are there?
- How many adults do not wear glasses?
|
Number |
Men |
Women |
Total |
174 |
4 u |
6 p |
Wear glasses |
35 |
1 u |
1 p |
No glasses |
|
3 u |
5 p |
(a)
Number of men = 4 u
Number of women = 6 p
4 u + 6 p = 174 --- (1)
1 u + 1 p = 35 --- (2)
(2)
x 4 4 u + 4 p = 140 --- (3)
(1) - (3)
(4 u + 6 p) - (4 u + 4 p) = 174 - 140
4 u + 6 p - 4 u - 4 p = 34
2 p = 34
1 p = 34 ÷ 2 = 17
Substitute 1 p = 17 into (2).
1 u + 1 p = 35
1 u + 17 = 35
1 u = 35 - 17 = 18
Number of men
= 4 u
= 4 x 18
= 72
(b)
Number of women
= 6 p
= 6 x 17
= 102
(c)
Number of men who do not wear glasses
= 4 u - 1 u
= 3 u
Number of women who do not wear glasses
= 6 p - 1 p
= 5 p
Number of adults who do not wear glasses
= 174 - 35
= 139
Answer(s): (a) 72; (b) 102; (c) 139