149 students went for a singing competition and 67 of them achieved Gold certificates.
35 of the boys and
14 of the girls achieved Gold certificates. How many boys did not achieve Gold certificates?
| Girls |
Boys |
| 5 u |
4 p |
Achieved
Gold |
Did not achieve
Gold |
Achieved
Gold |
Did not achieve
Gold |
| 3 u |
2 u |
1 p |
3 p |
Number of students who did not achieve Gold certificates
= 149 - 67
= 82
3 u + 1 p = 67
1 p = 67 - 3 u --- (1)
2 u + 3 p = 82
3 p = 82 - 2 u --- (2)
Make p the same.
(1)
x33 p = 201 - 9 u --- (3)
(2) = (3)
82 - 2 u = 201 - 9 u
9 u - 2 u = 201 - 82
7 u = 119
1 u = 119 ÷ 7 = 17
Number of girls who did not achieve Gold certificates
= 2 u
= 2 x 17
= 34
Number of boys who did not achieve Gold certificates
= 82 - 34
= 48
Answer(s): 48
