213 adults are in a school.
15 of the women and
18 of the men wear glasses.
33 adults wear glasses.
- How many women are there?
- How many men are there?
- How many adults do not wear glasses?
|
Number |
Women |
Men |
Total |
213 |
5 u |
8 p |
Wear glasses |
33 |
1 u |
1 p |
No glasses |
|
4 u |
7 p |
(a)
Number of women = 5 u
Number of men = 8 p
5 u + 8 p = 213 --- (1)
1 u + 1 p = 33 --- (2)
(2)
x 5 5 u + 5 p = 165 --- (3)
(1) - (3)
(5 u + 8 p) - (5 u + 5 p) = 213 - 165
5 u + 8 p - 5 u - 5 p = 48
3 p = 48
1 p = 48 ÷ 3 = 16
Substitute 1 p = 16 into (2).
1 u + 1 p = 33
1 u + 16 = 33
1 u = 33 - 16 = 17
Number of women
= 5 u
= 5 x 17
= 85
(b)
Number of men
= 8 p
= 8 x 16
= 128
(c)
Number of women who do not wear glasses
= 5 u - 1 u
= 4 u
Number of men who do not wear glasses
= 8 p - 1 p
= 7 p
Number of adults who do not wear glasses
= 213 - 33
= 180
Answer(s): (a) 85; (b) 128; (c) 180