115 students went for a dancing competition and 61 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
= 115 - 61
= 54
3 u + 1 p = 61
1 p = 61 - 3 u --- (1)
2 u + 2 p = 54
2 p = 54 - 2 u --- (2)
Make p the same.
(1)
x22 p = 122 - 6 u --- (3)
(2) = (3)
54 - 2 u = 122 - 6 u
6 u - 2 u = 122 - 54
4 u = 68
1 u = 68 ÷ 4 = 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
= 54 - 34
= 20
Answer(s): 20