If A + B = 12, and B + C = 16, What is the value of A + C?
A. -4
B. -28
C. 4
D. 28
E. The answer cannot be determined from the given information.
a + b = 12
b + c = 16
a - c = -4
I can not find a+c
Well, A + B = 12 and B + C = 16. So, we can isolate A by subtracting B from both sides of the first equation, which gives us A = 12 - B. Now, let's substitute the value of A in terms of B into the second equation. It becomes 12 - B + C = 16. Simplifying that, we have C - B = 4. Finally, we can isolate C by adding B to both sides of the equation, resulting in C = B + 4. Now we have values for A in terms of B and C in terms of B, but since we don't know the value of B, we can't determine the value of A + C. So, the answer is E. The answer cannot be determined from the given information.
To find the value of A + C, we need to eliminate the variable B.
First, let's solve the first equation for A:
A + B = 12
Subtract B from both sides:
A = 12 - B
Next, let's solve the second equation for C:
B + C = 16
Subtract B from both sides:
C = 16 - B
Now we substitute these values into the expression A + C:
A + C = (12 - B) + (16 - B)
Expand the equation:
A + C = 12 - B + 16 - B
Combine like terms:
A + C = 28 - 2B
Since we cannot determine the value of B from the given information, we cannot find the value of A + C.
Therefore, the answer is (E) The answer cannot be determined from the given information.
To find the value of A + C, we need to look for a way to relate A and C using the given equations.
We know that A + B = 12 and B + C = 16.
To isolate A, we can subtract B from both sides of the first equation:
A = 12 - B.
Now, we can substitute this expression for A into the second equation:
(12 - B) + C = 16.
To simplify this equation, we can combine like terms:
C - B + 12 = 16.
Next, we can subtract 12 from both sides of the equation to isolate C:
C - B = 4.
Finally, we can rearrange the equation to express C in terms of A and B:
C = B + 4.
Now we can substitute this expression for C into the expression for A:
A + C = A + (B + 4).
By combining like terms, we get:
A + C = (A + B) + 4.
Now, substitute the value of A + B from the first equation:
A + C = 12 + 4.
Simplifying, we find:
A + C = 16.
Therefore, the value of A + C is 16. The answer is not among the provided options, so the correct answer would be:
F. 16