166 people are in a school.
15 of the males and
18 of the females wear glasses.
23 people wear glasses.
- How many males are there?
- How many females are there?
- How many people do not wear glasses?
|
Number |
Males |
Females |
Total |
166 |
5 u |
8 p |
Wear glasses |
23 |
1 u |
1 p |
No glasses |
|
4 u |
7 p |
(a)
Number of males = 5 u
Number of females = 8 p
5 u + 8 p = 166 --- (1)
1 u + 1 p = 23 --- (2)
(2)
x 5 5 u + 5 p = 115 --- (3)
(1) - (3)
(5 u + 8 p) - (5 u + 5 p) = 166 - 115
5 u + 8 p - 5 u - 5 p = 51
3 p = 51
1 p = 51 ÷ 3 = 17
Substitute 1 p = 17 into (2).
1 u + 1 p = 23
1 u + 17 = 23
1 u = 23 - 17 = 6
Number of males
= 5 u
= 5 x 6
= 30
(b)
Number of females
= 8 p
= 8 x 17
= 136
(c)
Number of males who do not wear glasses
= 5 u - 1 u
= 4 u
Number of females who do not wear glasses
= 8 p - 1 p
= 7 p
Number of people who do not wear glasses
= 166 - 23
= 143
Answer(s): (a) 30; (b) 136; (c) 143