168 adults are in a school.
14 of the men and
110 of the women wear glasses.
36 adults wear glasses.
- How many men are there?
- How many women are there?
- How many adults do not wear glasses?
|
Number |
Men |
Women |
Total |
168 |
4 u |
10 p |
Wear glasses |
36 |
1 u |
1 p |
No glasses |
|
3 u |
9 p |
(a)
Number of men = 4 u
Number of women = 10 p
4 u + 10 p = 168 --- (1)
1 u + 1 p = 36 --- (2)
(2)
x 4 4 u + 4 p = 144 --- (3)
(1) - (3)
(4 u + 10 p) - (4 u + 4 p) = 168 - 144
4 u + 10 p - 4 u - 4 p = 24
6 p = 24
1 p = 24 ÷ 6 = 4
Substitute 1 p = 4 into (2).
1 u + 1 p = 36
1 u + 4 = 36
1 u = 36 - 4 = 32
Number of men
= 4 u
= 4 x 32
= 128
(b)
Number of women
= 10 p
= 10 x 4
= 40
(c)
Number of men who do not wear glasses
= 4 u - 1 u
= 3 u
Number of women who do not wear glasses
= 10 p - 1 p
= 9 p
Number of adults who do not wear glasses
= 168 - 36
= 132
Answer(s): (a) 128; (b) 40; (c) 132