Problem 4. The sum of 4 numbers is 100. The sum of the first, third, and fourth is 65, and the sum of the first, second, and third is 78. Determine the addends, if the first addend is 10 less than the second.
Solution. If $a, b, c$ and $d$ are the first, second, third, and fourth numbers respectively, from the condition of the problem we have

$$
a+b+c+d=100
$$

Since $a+c+d=65$, we get $b+65=100$, hence $b=35$. On the other hand, from $a+b+c=78$, we get $78+d=100$, hence $d=22$. Since $a+10=b$, we get $a=35-10=25$. Now it is clear that $c=18$.