Question
Anastasia uses the equation p = 0.7(rh + 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?
h = (h equals StartFraction p Over 0.7 EndFraction minus b divided by r.– b)÷ r
h = h equals StartFraction p Over 0.7 EndFraction minus b divided by r.– b ÷ r
h = h equals left-parenthesis StartFraction p Over 0.7 EndFraction right-parenthesis divided by r minus b.÷ r – b
h = h equals StartFraction p minus b Over 0.7 EndFraction divided by r. ÷ r
What is an equivalent equation solved for h?
h = (h equals StartFraction p Over 0.7 EndFraction minus b divided by r.– b)÷ r
h = h equals StartFraction p Over 0.7 EndFraction minus b divided by r.– b ÷ r
h = h equals left-parenthesis StartFraction p Over 0.7 EndFraction right-parenthesis divided by r minus b.÷ r – b
h = h equals StartFraction p minus b Over 0.7 EndFraction divided by r. ÷ r
Answers
GPT-4o mini
To solve the equation \( p = 0.7(rh + b) \) for \( h \), let’s follow these steps:
1. Start with the original equation:
\[
p = 0.7(rh + b)
\]
2. Divide both sides by \( 0.7 \):
\[
\frac{p}{0.7} = rh + b
\]
3. Subtract \( b \) from both sides:
\[
\frac{p}{0.7} - b = rh
\]
4. Finally, divide both sides by \( r \) to isolate \( h \):
\[
h = \frac{\frac{p}{0.7} - b}{r}
\]
This simplifies to:
\[
h = \frac{p - 0.7b}{0.7r}
\]
Looking at the answer options you provided, the equivalent equation for \( h \) would most closely match:
- \( h = \frac{p}{0.7} - b \div r \)
However, since that notation seems unclear and potentially confusing in your options, if it's simply presented as \( h = \frac{p - b}{0.7r} \) rather than with transformations yielding incorrect grouping, it would be the best representative in more clear contexts.
None of the options appear to match exactly but the closest approach of rationalizing \( b \) and separating the fractions could lead to confusion. Please utilize the standard rearranged value provided here for further use.
1. Start with the original equation:
\[
p = 0.7(rh + b)
\]
2. Divide both sides by \( 0.7 \):
\[
\frac{p}{0.7} = rh + b
\]
3. Subtract \( b \) from both sides:
\[
\frac{p}{0.7} - b = rh
\]
4. Finally, divide both sides by \( r \) to isolate \( h \):
\[
h = \frac{\frac{p}{0.7} - b}{r}
\]
This simplifies to:
\[
h = \frac{p - 0.7b}{0.7r}
\]
Looking at the answer options you provided, the equivalent equation for \( h \) would most closely match:
- \( h = \frac{p}{0.7} - b \div r \)
However, since that notation seems unclear and potentially confusing in your options, if it's simply presented as \( h = \frac{p - b}{0.7r} \) rather than with transformations yielding incorrect grouping, it would be the best representative in more clear contexts.
None of the options appear to match exactly but the closest approach of rationalizing \( b \) and separating the fractions could lead to confusion. Please utilize the standard rearranged value provided here for further use.