1997 PMWC Problems/Problem T6

Problem

During a rebuilding project by contractors 'A', 'B' and 'C', there was a shortage of tractors. The contractors lent each other tractors as needed. At first, 'A' lent 'B' and 'C' as many tractors as they each already had. A few months later, 'B' lent 'A' and 'C' as many as they each already had. Still later, 'C' lent 'A' and 'B' as many as they each already had. By then each contractor had tractors. How many tractors did each contractor originally have?

Solution

After C doubles the number of tractors that A and B has, they each have 24 tractors. Therefore A and B must have previously had 12 tractors, and C must have had 24+12+12=48 tractors. This is after B doubled the number of tractors that A and C had, so A must have had 6 tractors, C must have had 24 tractors, and B must have had 12+6+24=42 tractors. This is after A doubled the number of tractors that B and C had, so B must have had 21 tractors, C must have had 12 tractors, and A must have had 6+21+12=39 tractors. Therefore in the beginning A had 39 tractors, B had 21 tractors, and C had 12 tractors.