160 students went for a dancing competition and 58 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
= 160 - 58
= 102
3 u + 1 p = 58
1 p = 58 - 3 u --- (1)
2 u + 4 p = 102
4 p = 102 - 2 u --- (2)
Make p the same.
(1)
x44 p = 232 - 12 u --- (3)
(2) = (3)
102 - 2 u = 232 - 12 u
12 u - 2 u = 232 - 102
10 u = 130
1 u = 130 ÷ 10 = 13
Number of boys who did not achieve Silver certificates
= 2 u
= 2 x 13
= 26
Number of girls who did not achieve Silver certificates
= 102 - 26
= 76
Answer(s): 76
