Find three consecutive odd numbers whose sum is $93$.

Find three consecutive even numbers whose sum is $246$.

The sum of three consecutive multiples of $7$ is $777$. Find these multiples.

Divide $534$ into three parts such that the second part will be $32$ less than twice the first, and the third will be $18$ more than the first.

Three times the smallest of three consecutive odd numbers decreased by $7$ equals twice the largest one. Find the numbers.

One number is $7$ more than another and its square is $77$ more than the square of the smaller number. What are the numbers?

The square of the greater of two consecutive even numbers exceeds the square of the smaller by $36$. Find the numbers.

The denominator of a fraction is $3$ more than the numerator. If $5$ is added to both parts, the resulting fraction is equivalent to $\frac{4}{5}$. Find the fraction.

The difference between two positive integers is $50$ and the ratio of these integers is $1:3$. Find these integers.