243 people are in a school.
13 of the females and
16 of the males wear glasses.
48 people wear glasses.
- How many females are there?
- How many males are there?
- How many people do not wear glasses?
|
Number |
Females |
Males |
Total |
243 |
3 u |
6 p |
Wear glasses |
48 |
1 u |
1 p |
No glasses |
|
2 u |
5 p |
(a)
Number of females = 3 u
Number of males = 6 p
3 u + 6 p = 243 --- (1)
1 u + 1 p = 48 --- (2)
(2)
x 3 3 u + 3 p = 144 --- (3)
(1) - (3)
(3 u + 6 p) - (3 u + 3 p) = 243 - 144
3 u + 6 p - 3 u - 3 p = 99
3 p = 99
1 p = 99 ÷ 3 = 33
Substitute 1 p = 33 into (2).
1 u + 1 p = 48
1 u + 33 = 48
1 u = 48 - 33 = 15
Number of females
= 3 u
= 3 x 15
= 45
(b)
Number of males
= 6 p
= 6 x 33
= 198
(c)
Number of females who do not wear glasses
= 3 u - 1 u
= 2 u
Number of males who do not wear glasses
= 6 p - 1 p
= 5 p
Number of people who do not wear glasses
= 243 - 48
= 195
Answer(s): (a) 45; (b) 198; (c) 195