203 adults are in a school.
14 of the women and
19 of the men wear glasses.
27 adults wear glasses.
- How many women are there?
- How many men are there?
- How many adults do not wear glasses?
|
Number |
Women |
Men |
Total |
203 |
4 u |
9 p |
Wear glasses |
27 |
1 u |
1 p |
No glasses |
|
3 u |
8 p |
(a)
Number of women = 4 u
Number of men = 9 p
4 u + 9 p = 203 --- (1)
1 u + 1 p = 27 --- (2)
(2)
x 4 4 u + 4 p = 108 --- (3)
(1) - (3)
(4 u + 9 p) - (4 u + 4 p) = 203 - 108
4 u + 9 p - 4 u - 4 p = 95
5 p = 95
1 p = 95 ÷ 5 = 19
Substitute 1 p = 19 into (2).
1 u + 1 p = 27
1 u + 19 = 27
1 u = 27 - 19 = 8
Number of women
= 4 u
= 4 x 8
= 32
(b)
Number of men
= 9 p
= 9 x 19
= 171
(c)
Number of women who do not wear glasses
= 4 u - 1 u
= 3 u
Number of men who do not wear glasses
= 9 p - 1 p
= 8 p
Number of adults who do not wear glasses
= 203 - 27
= 176
Answer(s): (a) 32; (b) 171; (c) 176