93 people are in a school.
13 of the females and
19 of the males wear glasses.
13 people wear glasses.
- How many females are there?
- How many males are there?
- How many people do not wear glasses?
|
Number |
Females |
Males |
Total |
93 |
3 u |
9 p |
Wear glasses |
13 |
1 u |
1 p |
No glasses |
|
2 u |
8 p |
(a)
Number of females = 3 u
Number of males = 9 p
3 u + 9 p = 93 --- (1)
1 u + 1 p = 13 --- (2)
(2)
x 3 3 u + 3 p = 39 --- (3)
(1) - (3)
(3 u + 9 p) - (3 u + 3 p) = 93 - 39
3 u + 9 p - 3 u - 3 p = 54
6 p = 54
1 p = 54 ÷ 6 = 9
Substitute 1 p = 9 into (2).
1 u + 1 p = 13
1 u + 9 = 13
1 u = 13 - 9 = 4
Number of females
= 3 u
= 3 x 4
= 12
(b)
Number of males
= 9 p
= 9 x 9
= 81
(c)
Number of females who do not wear glasses
= 3 u - 1 u
= 2 u
Number of males who do not wear glasses
= 9 p - 1 p
= 8 p
Number of people who do not wear glasses
= 93 - 13
= 80
Answer(s): (a) 12; (b) 81; (c) 80