119 people are in a school.
13 of the males and
15 of the females wear glasses.
35 people wear glasses.
- How many males are there?
- How many females are there?
- How many people do not wear glasses?
|
Number |
Males |
Females |
Total |
119 |
3 u |
5 p |
Wear glasses |
35 |
1 u |
1 p |
No glasses |
|
2 u |
4 p |
(a)
Number of males = 3 u
Number of females = 5 p
3 u + 5 p = 119 --- (1)
1 u + 1 p = 35 --- (2)
(2)
x 3 3 u + 3 p = 105 --- (3)
(1) - (3)
(3 u + 5 p) - (3 u + 3 p) = 119 - 105
3 u + 5 p - 3 u - 3 p = 14
2 p = 14
1 p = 14 ÷ 2 = 7
Substitute 1 p = 7 into (2).
1 u + 1 p = 35
1 u + 7 = 35
1 u = 35 - 7 = 28
Number of males
= 3 u
= 3 x 28
= 84
(b)
Number of females
= 5 p
= 5 x 7
= 35
(c)
Number of males who do not wear glasses
= 3 u - 1 u
= 2 u
Number of females who do not wear glasses
= 5 p - 1 p
= 4 p
Number of people who do not wear glasses
= 119 - 35
= 84
Answer(s): (a) 84; (b) 35; (c) 84