212 people are in a school.
14 of the males and
18 of the females wear glasses.
30 people wear glasses.
- How many males are there?
- How many females are there?
- How many people do not wear glasses?
|
Number |
Males |
Females |
Total |
212 |
4 u |
8 p |
Wear glasses |
30 |
1 u |
1 p |
No glasses |
|
3 u |
7 p |
(a)
Number of males = 4 u
Number of females = 8 p
4 u + 8 p = 212 --- (1)
1 u + 1 p = 30 --- (2)
(2)
x 4 4 u + 4 p = 120 --- (3)
(1) - (3)
(4 u + 8 p) - (4 u + 4 p) = 212 - 120
4 u + 8 p - 4 u - 4 p = 92
4 p = 92
1 p = 92 ÷ 4 = 23
Substitute 1 p = 23 into (2).
1 u + 1 p = 30
1 u + 23 = 30
1 u = 30 - 23 = 7
Number of males
= 4 u
= 4 x 7
= 28
(b)
Number of females
= 8 p
= 8 x 23
= 184
(c)
Number of males who do not wear glasses
= 4 u - 1 u
= 3 u
Number of females who do not wear glasses
= 8 p - 1 p
= 7 p
Number of people who do not wear glasses
= 212 - 30
= 182
Answer(s): (a) 28; (b) 184; (c) 182