P=25+3a-0.5ab, express a in terms of b and P

To express \( a \) in terms of \( b \) and \( P \) from the equation \( P = 25 + 3a - 0.5ab \), follow these steps:

### Step 1: Start with the original equation
\[
P = 25 + 3a - 0.5ab
\]

### Step 2: Move the constant term to the left side of the equation
\[
P - 25 = 3a - 0.5ab
\]

### Step 3: Factor out \( a \) from the terms on the right-hand side
\[
P - 25 = a(3 - 0.5b)
\]

### Step 4: Solve for \( a \)
\[
a = \frac{P - 25}{3 - 0.5b}
\]

So, the expression for \( a \) in terms of \( b \) and \( P \) is:
\[
a = \frac{P - 25}{3 - 0.5b}
\]

Would you like more details on this solution or have any questions?

Here are 5 related questions you might be interested in:
1. How do you solve for \( b \) in terms of \( a \) and \( P \)?
2. What happens to \( a \) as \( b \) approaches 6?
3. How can you find the value of \( b \) that maximizes or minimizes \( a \)?
4. What is the significance of the denominator \( 3 - 0.5b \) in this equation?
5. Can you determine the values of \( P \) and \( b \) that make \( a \) undefined?

**Tip:** When solving for a variable, factor out common terms to simplify the equation before isolating the desired variable.

Learn how to express variable a in terms of variables b and P from the equation P = 25 + 3a - 0.5ab. This problem involves solving a linear equation for a specific variable, covering algebraic concepts such as linear equations and variable isolation. Suitable for students in Grades 10-12.

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