171 people are in a school.
15 of the females and
17 of the males wear glasses.
25 people wear glasses.
- How many females are there?
- How many males are there?
- How many people do not wear glasses?
|
Number |
Females |
Males |
Total |
171 |
5 u |
7 p |
Wear glasses |
25 |
1 u |
1 p |
No glasses |
|
4 u |
6 p |
(a)
Number of females = 5 u
Number of males = 7 p
5 u + 7 p = 171 --- (1)
1 u + 1 p = 25 --- (2)
(2)
x 5 5 u + 5 p = 125 --- (3)
(1) - (3)
(5 u + 7 p) - (5 u + 5 p) = 171 - 125
5 u + 7 p - 5 u - 5 p = 46
2 p = 46
1 p = 46 ÷ 2 = 23
Substitute 1 p = 23 into (2).
1 u + 1 p = 25
1 u + 23 = 25
1 u = 25 - 23 = 2
Number of females
= 5 u
= 5 x 2
= 10
(b)
Number of males
= 7 p
= 7 x 23
= 161
(c)
Number of females who do not wear glasses
= 5 u - 1 u
= 4 u
Number of males who do not wear glasses
= 7 p - 1 p
= 6 p
Number of people who do not wear glasses
= 171 - 25
= 146
Answer(s): (a) 10; (b) 161; (c) 146