64 people are in a school.
14 of the females and
19 of the males wear glasses.
11 people wear glasses.
- How many females are there?
- How many males are there?
- How many people do not wear glasses?
|
Number |
Females |
Males |
Total |
64 |
4 u |
9 p |
Wear glasses |
11 |
1 u |
1 p |
No glasses |
|
3 u |
8 p |
(a)
Number of females = 4 u
Number of males = 9 p
4 u + 9 p = 64 --- (1)
1 u + 1 p = 11 --- (2)
(2)
x 4 4 u + 4 p = 44 --- (3)
(1) - (3)
(4 u + 9 p) - (4 u + 4 p) = 64 - 44
4 u + 9 p - 4 u - 4 p = 20
5 p = 20
1 p = 20 ÷ 5 = 4
Substitute 1 p = 4 into (2).
1 u + 1 p = 11
1 u + 4 = 11
1 u = 11 - 4 = 7
Number of females
= 4 u
= 4 x 7
= 28
(b)
Number of males
= 9 p
= 9 x 4
= 36
(c)
Number of females who do not wear glasses
= 4 u - 1 u
= 3 u
Number of males who do not wear glasses
= 9 p - 1 p
= 8 p
Number of people who do not wear glasses
= 64 - 11
= 53
Answer(s): (a) 28; (b) 36; (c) 53