152 pupils went for a singing competition and 66 of them achieved Gold certificates.
35 of the girls and
14 of the boys achieved Gold certificates. How many girls did not achieve Gold certificates?
| Boys |
Girls |
| 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 pupils who did not achieve Gold certificates
= 152 - 66
= 86
3 u + 1 p = 66
1 p = 66 - 3 u --- (1)
2 u + 3 p = 86
3 p = 86 - 2 u --- (2)
Make p the same.
(1)
x33 p = 198 - 9 u --- (3)
(2) = (3)
86 - 2 u = 198 - 9 u
9 u - 2 u = 198 - 86
7 u = 112
1 u = 112 ÷ 7 = 16
Number of boys who did not achieve Gold certificates
= 2 u
= 2 x 16
= 32
Number of girls who did not achieve Gold certificates
= 86 - 32
= 54
Answer(s): 54
