Answer:
AI-generated answer
To find the values of A, B, and C in the given equations, we can start by substituting the values of A and B in terms of C into the equation A + B + C + C = 180.
1. Given: A + B + C + C = 180
Substituting A = 2C + B and B = 2C - 25 into the equation:
(2C + B) + (2C - 25) + C + C = 180
Simplifying the equation:
5C - 25 + 2C + 2C = 180
Combining like terms:
9C - 25 = 180
2. Now, let's solve for C.
Adding 25 to both sides of the equation:
9C = 180 + 25
9C = 205
Dividing both sides of the equation by 9:
C = 205 / 9
Simplifying the fraction:
C ≈ 22.78
3. Next, let's find the values of A and B using the given equations.
Substituting the value of C back into the equation B = 2C - 25:
B = 2(22.78) - 25
Calculating:
B ≈ 45.56 - 25
B ≈ 20.56
Substituting the value of C into the equation A = 2C + B:
A = 2(22.78) + 20.56
Calculating:
A ≈ 45.56 + 20.56
A ≈ 66.12
4. Finally, let's check if the equation 2C + B = A holds true.
Substituting the values of A, B, and C into the equation:
2(22.78) + 20.56 = 66.12
Calculating:
45.56 + 20.56 = 66.12
66.12 = 66.12
Since both sides of the equation are equal, the equation 2C + B = A is satisfied.
Therefore, the values of A, B, and C are approximately:
A ≈ 66.12
B ≈ 20.56
C ≈ 22.78
Explanation: