170 students went for a spelling test and 74 of them achieved Gold certificates.
35 of the girls and
15 of the boys achieved Gold certificates. How many girls did not achieve Gold certificates?
| Boys |
Girls |
| 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 students who did not achieve Gold certificates
= 170 - 74
= 96
3 u + 1 p = 74
1 p = 74 - 3 u --- (1)
2 u + 4 p = 96
4 p = 96 - 2 u --- (2)
Make p the same.
(1)
x44 p = 296 - 12 u --- (3)
(2) = (3)
96 - 2 u = 296 - 12 u
12 u - 2 u = 296 - 96
10 u = 200
1 u = 200 ÷ 10 = 20
Number of boys who did not achieve Gold certificates
= 2 u
= 2 x 20
= 40
Number of girls who did not achieve Gold certificates
= 96 - 40
= 56
Answer(s): 56
