[Rehema123]

There's a tug-of-war contest between machines and Michael had tickets to watch. In the first contest two dump trucks and a sand transporter beat a cement mixer. In the second contest, one dump truck and two sand transporters lost to a bulldozer. Unfortunately, Michael didn't get to watch the final contest. All he know was that the match-up was a sand transporter and a cement mixer were against a bulldozer and a dump truck. Who won?

[jcaron2]

Let's use D, S, C, and B for the respective forces of a dump truck, sand transporter, cement mixer, and bulldozer.

In the first contest two dump trucks and a sand transporter beat a cement mixer

That means the cement mixer would have needed a little bit of extra help in order to tie the match. We don't know how much extra force it would have taken, but let's call it f1.

2D + S = C + f1

In the second contest, one dump truck and two sand transporters lost to a bulldozer.

Using the same logic, we can say that the dump truck and sand transporters would have needed a little bit of extra force (let's call it f2) in order to have tied the match.

D + 2S + f2 = B

All he know was that the match-up was a sand transporter and a cement mixer were against a bulldozer and a dump truck. Who won?

S + C ? B + D

To figure out whether the ? Is supposed to be < or >, you can just solve the first equation for C and plug in the result (in terms of D, S, and f1) in place of the C in this last inequality. Then, likewise, you can replace B with its equivalent from the second equation. At that point, it should be obvious which side is greater.