235 adults are in a school.
13 of the men and
15 of the women wear glasses.
49 adults wear glasses.
- How many men are there?
- How many women are there?
- How many adults do not wear glasses?
|
Number |
Men |
Women |
Total |
235 |
3 u |
5 p |
Wear glasses |
49 |
1 u |
1 p |
No glasses |
|
2 u |
4 p |
(a)
Number of men = 3 u
Number of women = 5 p
3 u + 5 p = 235 --- (1)
1 u + 1 p = 49 --- (2)
(2)
x 3 3 u + 3 p = 147 --- (3)
(1) - (3)
(3 u + 5 p) - (3 u + 3 p) = 235 - 147
3 u + 5 p - 3 u - 3 p = 88
2 p = 88
1 p = 88 ÷ 2 = 44
Substitute 1 p = 44 into (2).
1 u + 1 p = 49
1 u + 44 = 49
1 u = 49 - 44 = 5
Number of men
= 3 u
= 3 x 5
= 15
(b)
Number of women
= 5 p
= 5 x 44
= 220
(c)
Number of men who do not wear glasses
= 3 u - 1 u
= 2 u
Number of women who do not wear glasses
= 5 p - 1 p
= 4 p
Number of adults who do not wear glasses
= 235 - 49
= 186
Answer(s): (a) 15; (b) 220; (c) 186