180 adults are in a school.
14 of the women and
18 of the men wear glasses.
30 adults wear glasses.
- How many women are there?
- How many men are there?
- How many adults do not wear glasses?
|
Number |
Women |
Men |
Total |
180 |
4 u |
8 p |
Wear glasses |
30 |
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 = 180 --- (1)
1 u + 1 p = 30 --- (2)
(2)
x 4 4 u + 4 p = 120 --- (3)
(1) - (3)
(4 u + 8 p) - (4 u + 4 p) = 180 - 120
4 u + 8 p - 4 u - 4 p = 60
4 p = 60
1 p = 60 ÷ 4 = 15
Substitute 1 p = 15 into (2).
1 u + 1 p = 30
1 u + 15 = 30
1 u = 30 - 15 = 15
Number of women
= 4 u
= 4 x 15
= 60
(b)
Number of men
= 8 p
= 8 x 15
= 120
(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
= 180 - 30
= 150
Answer(s): (a) 60; (b) 120; (c) 150