Answer:
To solve the problem, let's break it down step by step:
1. Let's assume the number we're trying to find is "x".
2. "Two-thirds of a number" can be expressed as (2/3)x.
3. The problem states that when we increase "two-thirds of a number" by 2, the result is 10. So, we can write the equation as:
(2/3)x + 2 = 10
To isolate the variable "x", we need to get rid of the constant term on the left side of the equation. We can do this by subtracting 2 from both sides:
(2/3)x + 2 - 2 = 10 - 2
(2/3)x = 8
5. Now, to solve for "x", we need to get rid of the coefficient (2/3) in front of it. We can do this by multiplying both sides of the equation by the reciprocal of (2/3), which is (3/2):
(3/2)(2/3)x = (3/2)(8)
x = 12
Therefore, the number we're looking for is 12.
To summarize:
To find the number, we set up the equation (2/3)x + 2 = 10, and then solve it step by step. By subtracting 2 from both sides and multiplying both sides by (3/2) to eliminate the coefficient, we find that the number is 12.
