143 people are in a school.
13 of the females and
110 of the males wear glasses.
22 people wear glasses.
- How many females are there?
- How many males are there?
- How many people do not wear glasses?
|
Number |
Females |
Males |
Total |
143 |
3 u |
10 p |
Wear glasses |
22 |
1 u |
1 p |
No glasses |
|
2 u |
9 p |
(a)
Number of females = 3 u
Number of males = 10 p
3 u + 10 p = 143 --- (1)
1 u + 1 p = 22 --- (2)
(2)
x 3 3 u + 3 p = 66 --- (3)
(1) - (3)
(3 u + 10 p) - (3 u + 3 p) = 143 - 66
3 u + 10 p - 3 u - 3 p = 77
7 p = 77
1 p = 77 ÷ 7 = 11
Substitute 1 p = 11 into (2).
1 u + 1 p = 22
1 u + 11 = 22
1 u = 22 - 11 = 11
Number of females
= 3 u
= 3 x 11
= 33
(b)
Number of males
= 10 p
= 10 x 11
= 110
(c)
Number of females who do not wear glasses
= 3 u - 1 u
= 2 u
Number of males who do not wear glasses
= 10 p - 1 p
= 9 p
Number of people who do not wear glasses
= 143 - 22
= 121
Answer(s): (a) 33; (b) 110; (c) 121