Problem 1. The sum of three numbers is 300. The first is twice as large as the second, and the third is equal to the sum of the first and second. What are these numbers?
Solution. From the condition of the problem, we have $a+b+c=300, a=2b$, $c=a+b$. From the first and third equations, it follows that $c=300:2=150$, and thus $a+b=150$. Then, from the last equation and the second, we get $3b=150$, from which $b=150:3=50$. Finally, from the second equation, we have $a=2b=2 \cdot 50=100$. Therefore, the required numbers are 100, 50, and 150.