208 adults are in a school.
13 of the women and
110 of the men wear glasses.
32 adults wear glasses.
- How many women are there?
- How many men are there?
- How many adults do not wear glasses?
|
Number |
Women |
Men |
Total |
208 |
3 u |
10 p |
Wear glasses |
32 |
1 u |
1 p |
No glasses |
|
2 u |
9 p |
(a)
Number of women = 3 u
Number of men = 10 p
3 u + 10 p = 208 --- (1)
1 u + 1 p = 32 --- (2)
(2)
x 3 3 u + 3 p = 96 --- (3)
(1) - (3)
(3 u + 10 p) - (3 u + 3 p) = 208 - 96
3 u + 10 p - 3 u - 3 p = 112
7 p = 112
1 p = 112 ÷ 7 = 16
Substitute 1 p = 16 into (2).
1 u + 1 p = 32
1 u + 16 = 32
1 u = 32 - 16 = 16
Number of women
= 3 u
= 3 x 16
= 48
(b)
Number of men
= 10 p
= 10 x 16
= 160
(c)
Number of women who do not wear glasses
= 3 u - 1 u
= 2 u
Number of men who do not wear glasses
= 10 p - 1 p
= 9 p
Number of adults who do not wear glasses
= 208 - 32
= 176
Answer(s): (a) 48; (b) 160; (c) 176