Anastasia uses the equation $p=0.7(r h+b)$ to estimate the amount of take-home pay, $p$, for $h$ hours worked at a rate of $r$ dollars per hour and any bonus received, $b$. What is an equivalent equation solved for h?
A. $h=\left(\frac{p}{0.7}-b\right) \div r$
B. $h=\frac{p}{0.7}-b \div r$
C. $h=\left(\frac{p}{0.7}\right) \div r-b$
D. $h=\frac{p-b}{0.7} \div r$
Answer (1)
Isolate h in the equation p = 0.7 ( r h + b ) .
Divide both sides by 0.7: 0.7 p = r h + b .
Subtract b from both sides: 0.7 p − b = r h .
Divide both sides by r : h = ( 0.7 p − b ) ÷ r .
The equivalent equation solved for h is h = ( 0.7 p − b ) ÷ r .
Explanation
Understanding the Problem We are given the equation p = 0.7 ( r h + b ) and we want to solve for h . This means we want to isolate h on one side of the equation.
Dividing by 0.7 First, divide both sides of the equation by 0.7: 0.7 p = r h + b
Subtracting b Next, subtract b from both sides: 0.7 p − b = r h
Dividing by r Finally, divide both sides by r : r 0.7 p − b = h This can be rewritten as: h = ( 0.7 p − b ) ÷ r
Final Answer Therefore, the equivalent equation solved for h is: h = ( 0.7 p − b ) ÷ r
Examples
Understanding how to rearrange formulas is essential in many real-world applications. For instance, in physics, you might use a formula to calculate the velocity of an object. If you know the distance and time but need to find the acceleration, you would rearrange the formula to solve for acceleration. Similarly, in finance, you can rearrange interest formulas to determine the principal amount needed to achieve a specific return on investment. These skills are crucial for problem-solving and making informed decisions in various fields.
