To solve the given equation [tex]\( p = 0.7(r h + b) \)[/tex] for [tex]\( h \)[/tex], follow these steps:
Step 1: Start with the given equation:
[tex]\[ p = 0.7(r h + b) \][/tex]
Step 2: Isolate the term involving [tex]\( h \)[/tex]. First, divide both sides by 0.7:
[tex]\[ \frac{p}{0.7} = r h + b \][/tex]
Step 3: Subtract the bonus term [tex]\( b \)[/tex] from both sides to further isolate the [tex]\( r h \)[/tex] term:
[tex]\[ \frac{p}{0.7} - b = r h \][/tex]
Step 4: Finally, solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( r \)[/tex]:
[tex]\[ h = \frac{\frac{p}{0.7} - b}{r} \][/tex]
This simplifies to:
[tex]\[ h = \frac{p}{0.7 r} - \frac{b}{r} \][/tex]
The equivalent form of this solution is:
[tex]\[ h = \frac{-b + 1.42857142857143 p}{r} \][/tex]
Therefore, the correct answer among the given options is:
[tex]\[ h = \left( \frac{p}{0.7} - b \right) \div r \][/tex]
