FMM7

Sharing Dump Trucks

Problem

Three neighboring construction sites are sharing dump trucks (due to an equipment shortage).

The first site lends the second and third as many dump trucks as they each already had. A few months later, the second lent the first and third as many dump trucks as they each had. Still later, the third lent the first and second as many as they each already had. Each construction site now had 24 dump trucks.

How many dump trucks did each site originally have?

Solution

Solve the problem backwards:

First / Second / Third

24 + 24 + 24 = 72
12 + 12 + 48 = 72
 6 + 42 + 24 = 72
39 + 21 + 12 = 72

Last line is the answer.