83 students went for a physical fitness test and 41 of them achieved Gold certificates.
35 of the boys and
13 of the girls achieved Gold certificates. How many boys did not achieve Gold certificates?
Girls |
Boys |
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 students who did not achieve Gold certificates
= 83 - 41
= 42
3 u + 1 p = 41
1 p = 41 - 3 u --- (1)
2 u + 2 p = 42
2 p = 42 - 2 u --- (2)
Make p the same.
(1)
x22 p = 82 - 6 u --- (3)
(2) = (3)
42 - 2 u = 82 - 6 u
6 u - 2 u = 82 - 42
4 u = 40
1 u = 40 ÷ 4 = 10
Number of girls who achieved Gold certificates
= 3 u
= 3 x 10
= 30
Number of boys who achieved Gold certificates
= 41 - 30
= 11
Answer(s): 11