Solve this mathematical hard quiz !

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

Step 1: Solve for AAA
We start with the first equation:

A+A=20A + A = 20A+A=20

This simplifies to:

2A=202A = 202A=20

By dividing both sides by 2:

A=10A = 10A=10

Step 2: Solve for BBB
Next, we move to the second equation:

B+B=10B + B = 10B+B=10

This simplifies to:

2B=102B = 102B=10

By dividing both sides by 2:

B=5B = 5B=5

Step 3: Solve for CCC
Now, we solve for CCC using the third equation:

C+C=8C + C = 8C+C=8

This simplifies to:

2C=82C = 82C=8

By dividing both sides by 2:

C=4C = 4C=4

Step 4: Apply the values to the final equation
Now that we have the values for AAA, BBB, and CCC, we can substitute them into the final equation A+B×CA + B \times CA+B×C:

A+B×CA + B \times CA+B×C

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

10+5×410 + 5 \times 410+5×4

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

5×4=205 \times 4 = 205×4=20

Now we add:

10+20=3010 + 20 = 3010+20=30

Final Answer:
The solution to A+B×CA + B \times CA+B×C is:

303030

Explanation Summary:
AAA is found by solving A+A=20A + A = 20A+A=20, resulting in A=10A = 10A=10.
BBB is found by solving B+B=10B + B = 10B+B=10, resulting in B=5B = 5B=5.
CCC is found by solving C+C=8C + C = 8C+C=8, resulting in C=4C = 4C=4.
Substituting these values into A+B×CA + B \times CA+B×C and applying the order of operations leads to the final answer of 30