174 people are in a school.
14 of the females and
16 of the males wear glasses.
41 people wear glasses.
- How many females are there?
- How many males are there?
- How many people do not wear glasses?
|
Number |
Females |
Males |
Total |
174 |
4 u |
6 p |
Wear glasses |
41 |
1 u |
1 p |
No glasses |
|
3 u |
5 p |
(a)
Number of females = 4 u
Number of males = 6 p
4 u + 6 p = 174 --- (1)
1 u + 1 p = 41 --- (2)
(2)
x 4 4 u + 4 p = 164 --- (3)
(1) - (3)
(4 u + 6 p) - (4 u + 4 p) = 174 - 164
4 u + 6 p - 4 u - 4 p = 10
2 p = 10
1 p = 10 ÷ 2 = 5
Substitute 1 p = 5 into (2).
1 u + 1 p = 41
1 u + 5 = 41
1 u = 41 - 5 = 36
Number of females
= 4 u
= 4 x 36
= 144
(b)
Number of males
= 6 p
= 6 x 5
= 30
(c)
Number of females who do not wear glasses
= 4 u - 1 u
= 3 u
Number of males who do not wear glasses
= 6 p - 1 p
= 5 p
Number of people who do not wear glasses
= 174 - 41
= 133
Answer(s): (a) 144; (b) 30; (c) 133