Problem 69 - College Algebra Essentials

Question

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$B=\frac{F}{S-V} \text { for } S$$

Step-by-Step Solution

Answer

\(S=\frac{F}{B}+V\)

Step 1: Isolation of the denominator

Begin by getting the denominator on its own on one side. We can achieve this by multiplying both sides of the equation by \(S-V\). This gives us: \(B(S-V)=F\).

Step 2: Distribute B

Next, distribute 'B' on the left side of the equation to both 'S' and '-V'. This transforms the equation into: \(BS-BV=F\).

Step 3: Solve for S

.Our end goal is to solve for ‘S’. So, bring all the terms including ‘S’ on one side and the rest on the other side. This gives us: \(BS=F+BV\). Now, factor out 'S' from the left side. This transforms the equation into: \(S(B)=F+BV\). Finally, divide both sides by 'B' to solve for 'S'. This gives the final equation as: \(S=\frac{F}{B}+V\).