\( \frac{a}{5}+\frac{b}{8}=1 \quad \) for \( b \)

To solve for \( b \) in the equation \( \frac{a}{5}+\frac{b}{8}=1 \), first, isolate \( \frac{b}{8} \): \[ \frac{b}{8} = 1 - \frac{a}{5} \] Next, multiply both sides by 8 to solve for \( b \): \[ b = 8\left( 1 - \frac{a}{5} \right) \] Now, simplify the equation: \[ b = 8 - \frac{8a}{5} \] So, the final expression for \( b \) is: \[ b = 8 - \frac{8a}{5} \] Now you’re ready to tackle problems involving relationships between variables in equations! Thinking practically, this kind of equation often arises in budgeting scenarios. For instance, if \( a \) represents money allocated to one category and you need to figure out how much is available for another category, substituting values into your rearranged formula can help plan your finances effectively.