99 students went for a singing competition and 49 of them achieved Gold certificates.
35 of the boys and
13 of the girls achieved Gold certificates. How many boys did not achieve Gold certificates?
| Girls |
Boys |
| 5 u |
3 p |
Achieved
Gold |
Did not achieve
Gold |
Achieved
Gold |
Did not achieve
Gold |
| 3 u |
2 u |
1 p |
2 p |
Number of students who did not achieve Gold certificates
= 99 - 49
= 50
3 u + 1 p = 49
1 p = 49 - 3 u --- (1)
2 u + 2 p = 50
2 p = 50 - 2 u --- (2)
Make p the same.
(1)
x22 p = 98 - 6 u --- (3)
(2) = (3)
50 - 2 u = 98 - 6 u
6 u - 2 u = 98 - 50
4 u = 48
1 u = 48 ÷ 4 = 12
Number of girls who achieved Gold certificates
= 3 u
= 3 x 12
= 36
Number of boys who achieved Gold certificates
= 49 - 36
= 13
Answer(s): 13
