Question 130898
3b+2a+1o=1.8
4b+3a+3o=3.05
6b+5a+4o=4.65

one way to solve is to make a matrix and reduce, using rules including - you can switch rows, you can multiply all four elements in a row by a constant, you can add or subtract one row from another row:

3 2 1 1.8
4 3 3 3.05
6 5 4 4.65

graphing calculators will do this for you. on my ti-89, i enter:
rref([3,2,1,1.8;4,3,3,3.05;6,5,4,4.65])

it returns:
1 0 0 .2
0 1 0 .45
0 0 1 .3

this means
1b+0a+0o=.2
0b+1a+0o=.45
0b+0a+1o=.3

so bananas cost $0.20, apples cost $0.45, and oranges cost $0.30.

I'd buy 'em.