47 adults are in a school.
13 of the men and
110 of the women wear glasses.
11 adults wear glasses.
- How many men are there?
- How many women are there?
- How many adults do not wear glasses?
|
Number |
Men |
Women |
Total |
47 |
3 u |
10 p |
Wear glasses |
11 |
1 u |
1 p |
No glasses |
|
2 u |
9 p |
(a)
Number of men = 3 u
Number of women = 10 p
3 u + 10 p = 47 --- (1)
1 u + 1 p = 11 --- (2)
(2)
x 3 3 u + 3 p = 33 --- (3)
(1) - (3)
(3 u + 10 p) - (3 u + 3 p) = 47 - 33
3 u + 10 p - 3 u - 3 p = 14
7 p = 14
1 p = 14 ÷ 7 = 2
Substitute 1 p = 2 into (2).
1 u + 1 p = 11
1 u + 2 = 11
1 u = 11 - 2 = 9
Number of men
= 3 u
= 3 x 9
= 27
(b)
Number of women
= 10 p
= 10 x 2
= 20
(c)
Number of men who do not wear glasses
= 3 u - 1 u
= 2 u
Number of women who do not wear glasses
= 10 p - 1 p
= 9 p
Number of adults who do not wear glasses
= 47 - 11
= 36
Answer(s): (a) 27; (b) 20; (c) 36