Answer:
Explanation:
Let's solve the problem step by step:
1) Let's assume the integer we are thinking of is "x."
2) Half of this integer is equal to x/2.
3) One third of the next integer is equal to (x+1)/3. This is because we are considering the next integer, which is one more than the integer we are thinking of.
4) According to the problem, x/2 is 3 more than (x+1)/3. Mathematically, we can represent this as:
x/2 = (x+1)/3 + 3
5) To solve for x, let's simplify the equation by multiplying through by the least common denominator, which is 6:
6*(x/2) = 6*((x+1)/3 + 3)
3x = 2(x+1) + 18
6x = 4(x+1) + 36
6x = 4x + 4 + 36
6x = 4x + 40
2x = 40
x = 20
Therefore, the integer we were thinking of is 20.