To solve this problem step by step, we need to carefully analyze the equations given and work out the values of the variables $A$, $B$, and $C$, then apply them to find the value of $A+B\times C$.

Step 1: Solve for $A$

We start with the first equation:

$$A+A=20$$

This simplifies to:

$$2A=20$$

By dividing both sides by 2:

$$A=10$$

Step 2: Solve for $B$

Next, we move to the second equation:

$$B+B=10$$

This simplifies to:

$$2B=10$$

By dividing both sides by 2:

$$B=5$$

Step 3: Solve for $C$

Now, we solve for $C$ using the third equation:

$$C+C=8$$

This simplifies to:

$$2C=8$$

By dividing both sides by 2:

$$C=4$$

Step 4: Apply the values to the final equation

Now that we have the values for $A$, $B$, and $C$, we can substitute them into the final equation $A+B\times C$:

$$A+B\times C$$

Using the values $A=10$, $B=5$, and $C=4$:

$$10+5\times 4$$

According to the order of operations (PEMDAS/BODMAS), multiplication comes before addition, so we first multiply:

$$5\times 4=20$$

Now we add:

$$10+20=30$$

Final Answer:

The solution to $A+B\times C$ is:

$$30$$

Explanation Summary:

1. $A$ is found by solving $A+A=20$, resulting in $A=10$.
2. $B$ is found by solving $B+B=10$, resulting in $B=5$.
3. $C$ is found by solving $C+C=8$, resulting in $C=4$.
4. Substituting these values into $A+B\times C$ and applying the order of operations leads to the final answer of 30.