184 adults are in a school.
14 of the women and
18 of the men wear glasses.
37 adults wear glasses.
- How many women are there?
- How many men are there?
- How many adults do not wear glasses?
|
Number |
Women |
Men |
Total |
184 |
4 u |
8 p |
Wear glasses |
37 |
1 u |
1 p |
No glasses |
|
3 u |
7 p |
(a)
Number of women = 4 u
Number of men = 8 p
4 u + 8 p = 184 --- (1)
1 u + 1 p = 37 --- (2)
(2)
x 4 4 u + 4 p = 148 --- (3)
(1) - (3)
(4 u + 8 p) - (4 u + 4 p) = 184 - 148
4 u + 8 p - 4 u - 4 p = 36
4 p = 36
1 p = 36 ÷ 4 = 9
Substitute 1 p = 9 into (2).
1 u + 1 p = 37
1 u + 9 = 37
1 u = 37 - 9 = 28
Number of women
= 4 u
= 4 x 28
= 112
(b)
Number of men
= 8 p
= 8 x 9
= 72
(c)
Number of women who do not wear glasses
= 4 u - 1 u
= 3 u
Number of men who do not wear glasses
= 8 p - 1 p
= 7 p
Number of adults who do not wear glasses
= 184 - 37
= 147
Answer(s): (a) 112; (b) 72; (c) 147