154 students went for a singing competition and 70 of them achieved Silver certificates.
35 of the boys and
14 of the girls achieved Silver certificates. How many boys did not achieve Silver certificates?
| Girls |
Boys |
| 5 u |
4 p |
Achieved
Silver |
Did not achieve
Silver |
Achieved
Silver |
Did not achieve
Silver |
| 3 u |
2 u |
1 p |
3 p |
Number of students who did not achieve Silver certificates
= 154 - 70
= 84
3 u + 1 p = 70
1 p = 70 - 3 u --- (1)
2 u + 3 p = 84
3 p = 84 - 2 u --- (2)
Make p the same.
(1)
x33 p = 210 - 9 u --- (3)
(2) = (3)
84 - 2 u = 210 - 9 u
9 u - 2 u = 210 - 84
7 u = 126
1 u = 126 ÷ 7 = 18
Number of girls who did not achieve Silver certificates
= 2 u
= 2 x 18
= 36
Number of boys who did not achieve Silver certificates
= 84 - 36
= 48
Answer(s): 48
