The planned number increased 5 times by 22 more than the same tripled number. What is this number?

1. It is clear from the condition that it is convenient to solve the given task by an equation. Let’s take the unknown number as x. Then increased by 5 times, it will be 5x, and tripled by 3 times, it will be 3x.
2. Since 5x is 22 units more than 3x, then subtract 3x from 5x and get 22. Then we get the following equation:
5x – 3x = 22.
2x = 22,
x = 22/2,
x = 11.
3. Let’s check if the required number is found correctly. To do this, we substitute it into the original equation:
5 * 11 – 3 * 11 = 22,
55 – 33 = 22,
22 = 22, since this equality is not violated, it means that x is found correctly.
Answer: The intended number is 11.