135 pupils went for a singing competition and 55 of them achieved Gold certificates.
35 of the boys and
15 of the girls achieved Gold certificates. How many boys did not achieve Gold certificates?
| Girls |
Boys |
| 5 u |
5 p |
Achieved
Gold |
Did not achieve
Gold |
Achieved
Gold |
Did not achieve
Gold |
| 3 u |
2 u |
1 p |
4 p |
Number of pupils who did not achieve Gold certificates
= 135 - 55
= 80
3 u + 1 p = 55
1 p = 55 - 3 u --- (1)
2 u + 4 p = 80
4 p = 80 - 2 u --- (2)
Make p the same.
(1)
x44 p = 220 - 12 u --- (3)
(2) = (3)
80 - 2 u = 220 - 12 u
12 u - 2 u = 220 - 80
10 u = 140
1 u = 140 ÷ 10 = 14
Number of girls who achieved Gold certificates
= 3 u
= 3 x 14
= 42
Number of boys who achieved Gold certificates
= 55 - 42
= 13
Answer(s): 13
