139 adults are in a school.
15 of the men and
19 of the women wear glasses.
19 adults wear glasses.
- How many men are there?
- How many women are there?
- How many adults do not wear glasses?
|
Number |
Men |
Women |
Total |
139 |
5 u |
9 p |
Wear glasses |
19 |
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 = 139 --- (1)
1 u + 1 p = 19 --- (2)
(2)
x 5 5 u + 5 p = 95 --- (3)
(1) - (3)
(5 u + 9 p) - (5 u + 5 p) = 139 - 95
5 u + 9 p - 5 u - 5 p = 44
4 p = 44
1 p = 44 ÷ 4 = 11
Substitute 1 p = 11 into (2).
1 u + 1 p = 19
1 u + 11 = 19
1 u = 19 - 11 = 8
Number of men
= 5 u
= 5 x 8
= 40
(b)
Number of women
= 9 p
= 9 x 11
= 99
(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
= 139 - 19
= 120
Answer(s): (a) 40; (b) 99; (c) 120