a,b,c,d and e satisfy this system of equations:

2a+b+c+d+e = 6
a+2b+c+d+e = 12
a+b+2c+d+e = 24
a+b+c+2d+e = 48
a+b+c+d+2e = 96

Find 3d+2e without solving the above system.

Summing the 5 equations gives
6(a+b+c+d+e)=186
multiplying by 5/6 gives
5a+5b+5c+5d+5e=155   (1)

Add three times the fourth to twice the fifth gives
5a+5b+5c+8d+7e=336 (2)

Subtracting (1) from (2) gives
3d+2e=336-155=181

Posted by Jer on 2014-12-16 13:48:49