Apple collecting

Luke, Peter, and Tibor compared how many kilograms of apples they had collected. They found that the arithmetic mean of what Luke and Peter collected was 10 kg larger than Tibor's contribution, and the arithmetic means of what Luke and Tibor collected was 3 kg smaller than Peter's contribution. Find the difference between the arithmetic mean of what Peter and Tibor collected and Luke's contribution.

Correct answer:

x =  -7 kg

Step-by-step explanation:

$$\begin{gathered} (l+p)/2=10+t \\ (l+t)/2=p-3 \\ l+p=20+2t \\ l+t=2p-6 \\ p=20+2t-l \\ t=2p-6-l \\ p=l-8/3 \\ t=l-34/3 \\ x=(p+t)/2-l \\ x=(l-8/3+l-34/3)/2-l \\ x=(-8/3-34/3)/2=-7\text{kg} \end{gathered}$$

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