61 adults are in a school.
13 of the men and
17 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 |
61 |
3 u |
7 p |
Wear glasses |
11 |
1 u |
1 p |
No glasses |
|
2 u |
6 p |
(a)
Number of men = 3 u
Number of women = 7 p
3 u + 7 p = 61 --- (1)
1 u + 1 p = 11 --- (2)
(2)
x 3 3 u + 3 p = 33 --- (3)
(1) - (3)
(3 u + 7 p) - (3 u + 3 p) = 61 - 33
3 u + 7 p - 3 u - 3 p = 28
4 p = 28
1 p = 28 ÷ 4 = 7
Substitute 1 p = 7 into (2).
1 u + 1 p = 11
1 u + 7 = 11
1 u = 11 - 7 = 4
Number of men
= 3 u
= 3 x 4
= 12
(b)
Number of women
= 7 p
= 7 x 7
= 49
(c)
Number of men who do not wear glasses
= 3 u - 1 u
= 2 u
Number of women who do not wear glasses
= 7 p - 1 p
= 6 p
Number of adults who do not wear glasses
= 61 - 11
= 50
Answer(s): (a) 12; (b) 49; (c) 50