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Anastasia uses the equation [tex]p=0.7(rh+b)[/tex] to estimate the amount of take-home pay, [tex]p[/tex], for [tex]h[/tex] hours worked at a rate of [tex]r[/tex] dollars per hour and any bonus received, [tex]b[/tex].

What is an equivalent equation solved for [tex]h[/tex]?

A. [tex]h=\left(\frac{p}{0.7}-b\right) \div r[/tex]

B. [tex]h=\frac{p}{0.7}-b \div r[/tex]

C. [tex]h=\left(\frac{p}{0.7}\right)+r-b[/tex]

D. [tex]h=\frac{p-b}{0.7} \div r[/tex]

Sagot :

GinnyAnswer
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]
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