213 adults are in a school.
15 of the women and
17 of the men wear glasses.
35 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 |
7 p |
Wear glasses |
35 |
1 u |
1 p |
No glasses |
|
4 u |
6 p |
(a)
Number of women = 5 u
Number of men = 7 p
5 u + 7 p = 213 --- (1)
1 u + 1 p = 35 --- (2)
(2)
x 5 5 u + 5 p = 175 --- (3)
(1) - (3)
(5 u + 7 p) - (5 u + 5 p) = 213 - 175
5 u + 7 p - 5 u - 5 p = 38
2 p = 38
1 p = 38 ÷ 2 = 19
Substitute 1 p = 19 into (2).
1 u + 1 p = 35
1 u + 19 = 35
1 u = 35 - 19 = 16
Number of women
= 5 u
= 5 x 16
= 80
(b)
Number of men
= 7 p
= 7 x 19
= 133
(c)
Number of women who do not wear glasses
= 5 u - 1 u
= 4 u
Number of men who do not wear glasses
= 7 p - 1 p
= 6 p
Number of adults who do not wear glasses
= 213 - 35
= 178
Answer(s): (a) 80; (b) 133; (c) 178