170 pupils went for a singing competition and 70 of them achieved Silver certificates.
35 of the boys and
15 of the girls achieved Silver certificates. How many boys did not achieve Silver certificates?
| Girls |
Boys |
| 5 u |
5 p |
Achieved
Silver |
Did not achieve
Silver |
Achieved
Silver |
Did not achieve
Silver |
| 3 u |
2 u |
1 p |
4 p |
Number of pupils who did not achieve Silver certificates
= 170 - 70
= 100
3 u + 1 p = 70
1 p = 70 - 3 u --- (1)
2 u + 4 p = 100
4 p = 100 - 2 u --- (2)
Make p the same.
(1)
x44 p = 280 - 12 u --- (3)
(2) = (3)
100 - 2 u = 280 - 12 u
12 u - 2 u = 280 - 100
10 u = 180
1 u = 180 ÷ 10 = 18
Number of girls who did not achieve Silver certificates
= 2 u
= 2 x 18
= 36
Number of boys who did not achieve Silver certificates
= 100 - 36
= 64
Answer(s): 64
