A positive integer is 3 times another number.If we add 2 to the larger and 5 to the smaller, then one of them becomes 2 times the other.Find the smaller number.

Let's denote the smaller number as x. According to the problem, the larger number is 3 times the smaller number, so we can denote it as 3x.

The problem also states that if we add 2 to the larger number and 5 to the smaller number, one of them becomes twice the other. This gives us two possible equations:

1. 3x + 2 = 2 * (x + 5)
2. x + 5 = 2 * (3x + 2)

We need to solve these two equations separately and see which one gives us a positive integer solution for x.

1. Solving the first equation:

3x + 2 = 2x + 10 3x - 2x = 10 - 2 x = 8

2. Solving the second equation:

x + 5 = 6x + 4 5 - 4 = 6x - x 1 = 5x x = 1/5

The second equation gives us a non-integer solution for x, so it doesn't fit the problem's conditions. Therefore, the solution to the problem is x = 8, which is the smaller number.