105 students went for a dancing competition and 43 of them achieved Silver certificates.
35 of the girls and
15 of the boys achieved Silver certificates. How many girls did not achieve Silver certificates?
| Boys |
Girls |
| 5 u |
5 p |
Achieved
Silver |
Did not achieve
Silver |
Achieved
Silver |
Did not achieve
Silver |
| 3 u |
2 u |
1 p |
4 p |
Number of students who did not achieve Silver certificates
= 105 - 43
= 62
3 u + 1 p = 43
1 p = 43 - 3 u --- (1)
2 u + 4 p = 62
4 p = 62 - 2 u --- (2)
Make p the same.
(1)
x44 p = 172 - 12 u --- (3)
(2) = (3)
62 - 2 u = 172 - 12 u
12 u - 2 u = 172 - 62
10 u = 110
1 u = 110 ÷ 10 = 11
Number of boys who achieved Silver certificates
= 3 u
= 3 x 11
= 33
Number of girls who achieved Silver certificates
= 43 - 33
= 10
Answer(s): 10
