134 people are in a school.
14 of the males and
17 of the females wear glasses.
32 people wear glasses.
- How many males are there?
- How many females are there?
- How many people do not wear glasses?
|
Number |
Males |
Females |
Total |
134 |
4 u |
7 p |
Wear glasses |
32 |
1 u |
1 p |
No glasses |
|
3 u |
6 p |
(a)
Number of males = 4 u
Number of females = 7 p
4 u + 7 p = 134 --- (1)
1 u + 1 p = 32 --- (2)
(2)
x 4 4 u + 4 p = 128 --- (3)
(1) - (3)
(4 u + 7 p) - (4 u + 4 p) = 134 - 128
4 u + 7 p - 4 u - 4 p = 6
3 p = 6
1 p = 6 ÷ 3 = 2
Substitute 1 p = 2 into (2).
1 u + 1 p = 32
1 u + 2 = 32
1 u = 32 - 2 = 30
Number of males
= 4 u
= 4 x 30
= 120
(b)
Number of females
= 7 p
= 7 x 2
= 14
(c)
Number of males who do not wear glasses
= 4 u - 1 u
= 3 u
Number of females who do not wear glasses
= 7 p - 1 p
= 6 p
Number of people who do not wear glasses
= 134 - 32
= 102
Answer(s): (a) 120; (b) 14; (c) 102