111 pupils went for a dancing competition and 57 of them achieved Gold certificates.
35 of the girls and
13 of the boys achieved Gold certificates. How many girls did not achieve Gold certificates?
| Boys |
Girls |
| 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 pupils who did not achieve Gold certificates
= 111 - 57
= 54
3 u + 1 p = 57
1 p = 57 - 3 u --- (1)
2 u + 2 p = 54
2 p = 54 - 2 u --- (2)
Make p the same.
(1)
x22 p = 114 - 6 u --- (3)
(2) = (3)
54 - 2 u = 114 - 6 u
6 u - 2 u = 114 - 54
4 u = 60
1 u = 60 ÷ 4 = 15
Number of boys who achieved Gold certificates
= 3 u
= 3 x 15
= 45
Number of girls who achieved Gold certificates
= 57 - 45
= 12
Answer(s): 12
