To solve this problem step by step, we need to carefully analyze the equations given and work out the values of the variables AA, BB, and CC, then apply them to find the value of A+B×CA + B \times C.
Step 1: Solve for AA
We start with the first equation:
A+A=20A + A = 20
This simplifies to:
2A=202A = 20
By dividing both sides by 2:
A=10A = 10
Step 2: Solve for BB
Next, we move to the second equation:
B+B=10B + B = 10
This simplifies to:
2B=102B = 10
By dividing both sides by 2:
B=5B = 5
Step 3: Solve for CC
Now, we solve for CC using the third equation:
C+C=8C + C = 8
This simplifies to:
2C=82C = 8
By dividing both sides by 2:
C=4C = 4
Step 4: Apply the values to the final equation
Now that we have the values for AA, BB, and CC, we can substitute them into the final equation A+B×CA + B \times C:
A+B×CA + B \times C
Using the values A=10A = 10, B=5B = 5, and C=4C = 4:
10+5×410 + 5 \times 4
According to the order of operations (PEMDAS/BODMAS), multiplication comes before addition, so we first multiply:
5×4=205 \times 4 = 20
Now we add:
10+20=3010 + 20 = 30
Final Answer:
The solution to A+B×CA + B \times C is:
3030
Explanation Summary:
- AA is found by solving A+A=20A + A = 20, resulting in A=10A = 10.
- BB is found by solving B+B=10B + B = 10, resulting in B=5B = 5.
- CC is found by solving C+C=8C + C = 8, resulting in C=4C = 4.
- Substituting these values into A+B×CA + B \times C and applying the order of operations leads to the final answer of 30.
