81 adults are in a school.
15 of the men and
18 of the women wear glasses.
15 adults wear glasses.
- How many men are there?
- How many women are there?
- How many adults do not wear glasses?
| |
Number |
Men |
Women |
| Total |
81 |
5 u |
8 p |
| Wear glasses |
15 |
1 u |
1 p |
| No glasses |
|
4 u |
7 p |
(a)
Number of men = 5 u
Number of women = 8 p
5 u + 8 p = 81 --- (1)
1 u + 1 p = 15 --- (2)
(2)
x 5 5 u + 5 p = 75 --- (3)
(1) - (3)
(5 u + 8 p) - (5 u + 5 p) = 81 - 75
5 u + 8 p - 5 u - 5 p = 6
3 p = 6
1 p = 6 ÷ 3 = 2
Substitute 1 p = 2 into (2).
1 u + 1 p = 15
1 u + 2 = 15
1 u = 15 - 2 = 13
Number of men
= 5 u
= 5 x 13
= 65
(b)
Number of women
= 8 p
= 8 x 2
= 16
(c)
Number of men who do not wear glasses
= 5 u - 1 u
= 4 u
Number of women who do not wear glasses
= 8 p - 1 p
= 7 p
Number of adults who do not wear glasses
= 81 - 15
= 66
Answer(s): (a) 65; (b) 16; (c) 66
