A hand-held shopping basket 52.4 cm long has a 1.95-kg carton of milk at one end

Question

A hand-held shopping basket 52.4 cm long has a 1.95-kg carton of milk at one end, and a 0.739-kg box of cereal at the other end. Where (how far away from the center of the shopping basket) should a 1.93-kg container of orange juice be placed so that the basket balances at its center? Let the side of the cereal be positive and the side of the milk carton be negative.
I think this is a center of mass problem.
I wasnt sure what my professor ment by one side being negative and the other positive here. I used an arbitrary reference point of 1 meter away and i think I calculated the center of mass to be at 1.144M from this arbitray reference point ( 0.144 from what was my 1 meter milk). After I got that I wasnt sure how to solve for where the new mass of the OJ should be and Im afraid that the tip about the negative side versus the positive side also threw off my calculation. Any help would be appreciated.

Explanation / Answer

Since .739 kg box is lighter so initially the basket will have a tendency to topple towards the side where milk carton is placed. Suppose container of juice is placed at a distance of x cm from the centre towards the side of the cereal box. Therefore balancing moments from the centre of the basket (1.95 * 26.2) = (.739 * 26.2) + (1.93*x) x = (1.21 * 26.2)/1.93 = 16.44 cm from the centre

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