Paying for the firewood
Three friends cook over one fire and share the meal equally. The first brings 5 logs, the second brings 3 logs, and the third brings none. All 8 logs are burned. The third friend pays 8 dollars for his share of the wood.
How many dollars should go to the friend who brought 5 logs?
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
Each friend uses the same amount of wood. How much is that?
How much wood did each of the first two friends give to the third?
h
s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. The third friend pays for the wood he used, so the money should be split according to how much wood each of the others gave him, not according to how much they brought.
Step 1. Each friend uses a third of the 8 logs: logs.
Step 2. The first friend brought 5 and used , so gave to the third. The second brought 3 and gave .
Step 3. The third friend received logs for 8 dollars, so 3 dollars per log. The first friend gets dollars and the second 1 dollar.
The trap. Splitting 5 to 3 gives 5 and 3 dollars. But the first two friends also burned their own wood: only what they gave away should be paid for.