130 people are in a school.
15 of the males and
17 of the females wear glasses.
22 people wear glasses.
- How many males are there?
- How many females are there?
- How many people do not wear glasses?
|
Number |
Males |
Females |
Total |
130 |
5 u |
7 p |
Wear glasses |
22 |
1 u |
1 p |
No glasses |
|
4 u |
6 p |
(a)
Number of males = 5 u
Number of females = 7 p
5 u + 7 p = 130 --- (1)
1 u + 1 p = 22 --- (2)
(2)
x 5 5 u + 5 p = 110 --- (3)
(1) - (3)
(5 u + 7 p) - (5 u + 5 p) = 130 - 110
5 u + 7 p - 5 u - 5 p = 20
2 p = 20
1 p = 20 ÷ 2 = 10
Substitute 1 p = 10 into (2).
1 u + 1 p = 22
1 u + 10 = 22
1 u = 22 - 10 = 12
Number of males
= 5 u
= 5 x 12
= 60
(b)
Number of females
= 7 p
= 7 x 10
= 70
(c)
Number of males who do not wear glasses
= 5 u - 1 u
= 4 u
Number of females who do not wear glasses
= 7 p - 1 p
= 6 p
Number of people who do not wear glasses
= 130 - 22
= 108
Answer(s): (a) 60; (b) 70; (c) 108