145 adults are in a school.
13 of the women and
17 of the men wear glasses.
47 adults wear glasses.
- How many women are there?
- How many men are there?
- How many adults do not wear glasses?
|
Number |
Women |
Men |
Total |
145 |
3 u |
7 p |
Wear glasses |
47 |
1 u |
1 p |
No glasses |
|
2 u |
6 p |
(a)
Number of women = 3 u
Number of men = 7 p
3 u + 7 p = 145 --- (1)
1 u + 1 p = 47 --- (2)
(2)
x 3 3 u + 3 p = 141 --- (3)
(1) - (3)
(3 u + 7 p) - (3 u + 3 p) = 145 - 141
3 u + 7 p - 3 u - 3 p = 4
4 p = 4
1 p = 4 ÷ 4 = 1
Substitute 1 p = 1 into (2).
1 u + 1 p = 47
1 u + 1 = 47
1 u = 47 - 1 = 46
Number of women
= 3 u
= 3 x 46
= 138
(b)
Number of men
= 7 p
= 7 x 1
= 7
(c)
Number of women who do not wear glasses
= 3 u - 1 u
= 2 u
Number of men who do not wear glasses
= 7 p - 1 p
= 6 p
Number of adults who do not wear glasses
= 145 - 47
= 98
Answer(s): (a) 138; (b) 7; (c) 98