122 people are in a school.
13 of the males and
17 of the females wear glasses.
34 people wear glasses.
- How many males are there?
- How many females are there?
- How many people do not wear glasses?
|
Number |
Males |
Females |
Total |
122 |
3 u |
7 p |
Wear glasses |
34 |
1 u |
1 p |
No glasses |
|
2 u |
6 p |
(a)
Number of males = 3 u
Number of females = 7 p
3 u + 7 p = 122 --- (1)
1 u + 1 p = 34 --- (2)
(2)
x 3 3 u + 3 p = 102 --- (3)
(1) - (3)
(3 u + 7 p) - (3 u + 3 p) = 122 - 102
3 u + 7 p - 3 u - 3 p = 20
4 p = 20
1 p = 20 ÷ 4 = 5
Substitute 1 p = 5 into (2).
1 u + 1 p = 34
1 u + 5 = 34
1 u = 34 - 5 = 29
Number of males
= 3 u
= 3 x 29
= 87
(b)
Number of females
= 7 p
= 7 x 5
= 35
(c)
Number of males who do not wear glasses
= 3 u - 1 u
= 2 u
Number of females who do not wear glasses
= 7 p - 1 p
= 6 p
Number of people who do not wear glasses
= 122 - 34
= 88
Answer(s): (a) 87; (b) 35; (c) 88