253 people are in a school.
15 of the males and
17 of the females wear glasses.
43 people wear glasses.
- How many males are there?
- How many females are there?
- How many people do not wear glasses?
|
Number |
Males |
Females |
Total |
253 |
5 u |
7 p |
Wear glasses |
43 |
1 u |
1 p |
No glasses |
|
4 u |
6 p |
(a)
Number of males = 5 u
Number of females = 7 p
5 u + 7 p = 253 --- (1)
1 u + 1 p = 43 --- (2)
(2)
x 5 5 u + 5 p = 215 --- (3)
(1) - (3)
(5 u + 7 p) - (5 u + 5 p) = 253 - 215
5 u + 7 p - 5 u - 5 p = 38
2 p = 38
1 p = 38 ÷ 2 = 19
Substitute 1 p = 19 into (2).
1 u + 1 p = 43
1 u + 19 = 43
1 u = 43 - 19 = 24
Number of males
= 5 u
= 5 x 24
= 120
(b)
Number of females
= 7 p
= 7 x 19
= 133
(c)
Number of males who do not wear glasses
= 5 u - 1 u
= 4 u
Number of females who do not wear glasses
= 7 p - 1 p
= 6 p
Number of people who do not wear glasses
= 253 - 43
= 210
Answer(s): (a) 120; (b) 133; (c) 210