Answer:
Explanation:
Let the three-digit number be represented as $abc$, where $a$ is the hundreds digit, $b$ is the tens digit, and $c$ is the units digit.
From the problem, we have two equations:
Equation 1: $2a=b+2$
Equation 2: $c=3a$
We can use these equations to solve for $a$, $b$, and $c$.
Starting with Equation 1, we can isolate $b$ to get $b=2a-2$.
Next, we can substitute Equation 2 into Equation 1 to get $2a=3a-6+2$, which simplifies to $a=8$.
Using this value of $a$, we can now find $b$ and $c$. From Equation 2, we have $c=3a=24$. And from Equation 1, we have $b=2a-2=14$.
Thus, the original three-digit number is $abc=824$.
When we reverse the digits to get $cba=428$, we increase the number by 594, so we have $cba=abc+594=824+594=1418$.
Therefore, the answer is $\boxed{824}$.