253 adults are in a school.
15 of the men and
19 of the women wear glasses.
37 adults wear glasses.
- How many men are there?
- How many women are there?
- How many adults do not wear glasses?
|
Number |
Men |
Women |
Total |
253 |
5 u |
9 p |
Wear glasses |
37 |
1 u |
1 p |
No glasses |
|
4 u |
8 p |
(a)
Number of men = 5 u
Number of women = 9 p
5 u + 9 p = 253 --- (1)
1 u + 1 p = 37 --- (2)
(2)
x 5 5 u + 5 p = 185 --- (3)
(1) - (3)
(5 u + 9 p) - (5 u + 5 p) = 253 - 185
5 u + 9 p - 5 u - 5 p = 68
4 p = 68
1 p = 68 ÷ 4 = 17
Substitute 1 p = 17 into (2).
1 u + 1 p = 37
1 u + 17 = 37
1 u = 37 - 17 = 20
Number of men
= 5 u
= 5 x 20
= 100
(b)
Number of women
= 9 p
= 9 x 17
= 153
(c)
Number of men who do not wear glasses
= 5 u - 1 u
= 4 u
Number of women who do not wear glasses
= 9 p - 1 p
= 8 p
Number of adults who do not wear glasses
= 253 - 37
= 216
Answer(s): (a) 100; (b) 153; (c) 216