Solve each equation for the indicated variable. Round answers to two decimal places as necessary.
$\frac{B}{-23}-22=-35$
Answer (1)
Add 22 to both sides: − 23 B = − 13 .
Multiply both sides by -23: B = − 13 × − 23 .
Calculate the value of B: B = 299 .
The solution is 299 .
Explanation
Understanding the Problem We are given the equation − 23 B − 22 = − 35 and we need to solve for the variable B .
Isolating the Term with B First, we add 22 to both sides of the equation to isolate the term with B : − 23 B − 22 + 22 = − 35 + 22 − 23 B = − 13
Solving for B Next, we multiply both sides of the equation by -23 to solve for B : ( − 23 ) × − 23 B = − 13 × ( − 23 ) B = − 13 × ( − 23 )
Calculating the Value of B Now, we calculate the value of B : B = 299 Since the question asks to round the answer to two decimal places if necessary, and 299 is an integer, we can write it as 299.00.
Examples
In real-world scenarios, this type of equation can be used to determine an initial value before a percentage decrease. For example, if a stock price decreased by 22 points and is now at -35, and this decrease represents a fraction (1/23) of the original stock price, we can use this equation to find the original stock price. Understanding how to solve such equations helps in financial analysis and planning.
