Solve for $C$. $A=\frac{2}{3}(B+C)$
Answer (2)
Multiply both sides of the equation by 2 3 : 2 3 A = B + C .
Subtract B from both sides: C = 2 3 A − B .
The equation is now solved for C .
The final answer is C = 2 3 A − B .
Explanation
Understanding the Problem We are given the equation A = 3 2 ( B + C ) and our goal is to isolate C on one side of the equation. This involves using algebraic manipulations to undo the operations that are applied to C .
Multiplying by the Reciprocal First, we want to get rid of the fraction 3 2 that is multiplying the parentheses. To do this, we multiply both sides of the equation by the reciprocal of 3 2 , which is 2 3 . This gives us: 2 3 A = 2 3 × 3 2 ( B + C ) 2 3 A = B + C
Isolating C Now, we want to isolate C . Since B is being added to C , we subtract B from both sides of the equation: 2 3 A − B = B + C − B 2 3 A − B = C
Final Answer Therefore, we have solved for C in terms of A and B : C = 2 3 A − B
Examples
This type of equation manipulation is useful in many real-world scenarios. For example, if you are calculating the total cost of a project ( A ) which depends on the cost of materials ( B ) and labor ( C ), and you know the total cost and the cost of materials, you can use this formula to determine the cost of labor. Similarly, in physics, if you know the total energy ( A ) of a system and the potential energy ( B ), you can find the kinetic energy ( C ).
To isolate C in the equation A = 3 2 ( B + C ) , first multiply both sides by 2 3 to obtain 2 3 A = B + C . Then, subtract B from both sides to yield the final result C = 2 3 A − B .
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