150 pupils went for a dancing competition and 43 of them achieved Gold certificates.
25 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 |
2 u |
3 u |
1 p |
4 p |
Number of pupils who did not achieve Gold certificates
= 150 - 43
= 107
2 u + 1 p = 43
1 p = 43 - 2 u --- (1)
3 u + 4 p = 107
4 p = 107 - 3 u --- (2)
Make p the same.
(1)
x44 p = 172 - 8 u --- (3)
(2) = (3)
107 - 3 u = 172 - 8 u
8 u - 3 u = 172 - 107
5 u = 65
1 u = 65 ÷ 5 = 13
Number of girls who achieved Gold certificates
= 2 u
= 2 x 13
= 26
Number of boys who achieved Gold certificates
= 43 - 26
= 17
Answer(s): 17