156 adults are in a school.
14 of the men and
18 of the women wear glasses.
20 adults wear glasses.
- How many men are there?
- How many women are there?
- How many adults do not wear glasses?
|
Number |
Men |
Women |
Total |
156 |
4 u |
8 p |
Wear glasses |
20 |
1 u |
1 p |
No glasses |
|
3 u |
7 p |
(a)
Number of men = 4 u
Number of women = 8 p
4 u + 8 p = 156 --- (1)
1 u + 1 p = 20 --- (2)
(2)
x 4 4 u + 4 p = 80 --- (3)
(1) - (3)
(4 u + 8 p) - (4 u + 4 p) = 156 - 80
4 u + 8 p - 4 u - 4 p = 76
4 p = 76
1 p = 76 ÷ 4 = 19
Substitute 1 p = 19 into (2).
1 u + 1 p = 20
1 u + 19 = 20
1 u = 20 - 19 = 1
Number of men
= 4 u
= 4 x 1
= 4
(b)
Number of women
= 8 p
= 8 x 19
= 152
(c)
Number of men who do not wear glasses
= 4 u - 1 u
= 3 u
Number of women who do not wear glasses
= 8 p - 1 p
= 7 p
Number of adults who do not wear glasses
= 156 - 20
= 136
Answer(s): (a) 4; (b) 152; (c) 136