108 adults are in a school.
14 of the men and
18 of the women wear glasses.
25 adults wear glasses.
- How many men are there?
- How many women are there?
- How many adults do not wear glasses?
|
Number |
Men |
Women |
Total |
108 |
4 u |
8 p |
Wear glasses |
25 |
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 = 108 --- (1)
1 u + 1 p = 25 --- (2)
(2)
x 4 4 u + 4 p = 100 --- (3)
(1) - (3)
(4 u + 8 p) - (4 u + 4 p) = 108 - 100
4 u + 8 p - 4 u - 4 p = 8
4 p = 8
1 p = 8 ÷ 4 = 2
Substitute 1 p = 2 into (2).
1 u + 1 p = 25
1 u + 2 = 25
1 u = 25 - 2 = 23
Number of men
= 4 u
= 4 x 23
= 92
(b)
Number of women
= 8 p
= 8 x 2
= 16
(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
= 108 - 25
= 83
Answer(s): (a) 92; (b) 16; (c) 83