In Exercises 45–47, solve each formula for the specified variable. T = (A-P)/Pr for P

Verified step by step guidance

1. Start with the given formula: $T=\frac{A-P}{Pr}$. The goal is to solve for $P$.
2. Multiply both sides of the equation by $Pr$ to eliminate the denominator: $TPr=A-P$.
3. Rearrange the equation to isolate terms involving $P$ on one side. Add $P$ to both sides: $TPr+P=A$.
4. Factor out $P$ from the left-hand side: $P(Tr+1)=A$.
5. Divide both sides of the equation by $Tr+1$ to solve for $P$: $P=\frac{A}{Tr+1}$.

Key Concepts

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate a specific variable. This process includes operations such as addition, subtraction, multiplication, and division applied to both sides of the equation to maintain equality. Understanding how to manipulate equations is essential for solving for a variable, as it allows one to express the variable in terms of others.

Formulas and Variables

A formula is a mathematical relationship expressed in symbols, often involving multiple variables. In the given equation, T, A, P, and r are variables that represent different quantities. Recognizing the roles of these variables and how they interact within the formula is crucial for solving for the desired variable, in this case, P.

Isolating the Variable

Isolating the variable means rearranging the equation so that the variable of interest stands alone on one side. This often requires inverse operations to eliminate other variables from that side. In the context of the given formula, isolating P involves strategically applying algebraic operations to express P in terms of T, A, and r.