273 adults are in a school.
13 of the women and
19 of the men wear glasses.
49 adults wear glasses.
- How many women are there?
- How many men are there?
- How many adults do not wear glasses?
|
Number |
Women |
Men |
Total |
273 |
3 u |
9 p |
Wear glasses |
49 |
1 u |
1 p |
No glasses |
|
2 u |
8 p |
(a)
Number of women = 3 u
Number of men = 9 p
3 u + 9 p = 273 --- (1)
1 u + 1 p = 49 --- (2)
(2)
x 3 3 u + 3 p = 147 --- (3)
(1) - (3)
(3 u + 9 p) - (3 u + 3 p) = 273 - 147
3 u + 9 p - 3 u - 3 p = 126
6 p = 126
1 p = 126 ÷ 6 = 21
Substitute 1 p = 21 into (2).
1 u + 1 p = 49
1 u + 21 = 49
1 u = 49 - 21 = 28
Number of women
= 3 u
= 3 x 28
= 84
(b)
Number of men
= 9 p
= 9 x 21
= 189
(c)
Number of women who do not wear glasses
= 3 u - 1 u
= 2 u
Number of men who do not wear glasses
= 9 p - 1 p
= 8 p
Number of adults who do not wear glasses
= 273 - 49
= 224
Answer(s): (a) 84; (b) 189; (c) 224