Elementary Mathematics International Contest (IMC 2008) Solutions

Solution 2 :
3x + 2y = 32, y = (32 - 3x) / 2
4x + 3y = 44
4x + 3(32 - 3x) /2 = 44
8x + 96 - 9x = 88
x = 8
y = (32 - 24) / 2 = 4
2x + y = 16 + 4 = 20

Solution 3 :
sit + stand = 100, stand = 100 - sit.
0.75 stand + 0.25 sit = 70
0.75(100 - sit) + 0.25 sit = 70
75 - 0.75 sit + 0.25 sit = 70
5 = 0.50 sit
sit = 10

Solution 4 :
(110000 - 100000) / 3600 x t = (17 + 3)
t = 20 x 3600 / 10000 =  7.2 seconds