Question
Which situation could the equation 5v=2v+42 represent?(1 point) Responses Plan X costs $5 per visit. Plan Y costs $42 per month and $2 per visit. How many visits, v, would Leila need to make per month for these options to be equal in price? Plan X costs $5 per visit. Plan Y costs $42 per month and $2 per visit. How many visits, v , would Leila need to make per month for these options to be equal in price? Plan X costs $5 per visit. Plan Y costs $2 per month and $42 per visit. How many visits, v, would Leila need to make per month for these options to be equal in price? Plan X costs $5 per visit. Plan Y costs $2 per month and $42 per visit. How many visits, v , would Leila need to make per month for these options to be equal in price? Plan X costs $5 per month. Plan Y costs $42 per month and $2 per visit. How many visits, v, would Leila need to make per month for these options to be equal in price? Plan X costs $5 per month. Plan Y costs $42 per month and $2 per visit. How many visits, v , would Leila need to make per month for these options to be equal in price? Plan X costs $5 per visit plus $42 per month. Plan Y costs $2 per visit plus $42 per month. How many visits, v, would Leila need to make per month for these options to be equal in price?
Answers
GPT-4o mini
To determine which scenario the equation \(5v = 2v + 42\) represents, we first need to break down the expression in relation to the costs described.
The equation can be rearranged as follows:
1. Start with the original equation: \(5v = 2v + 42\).
2. Subtract \(2v\) from both sides:
\[
5v - 2v = 42 \implies 3v = 42.
\]
3. Divide both sides by 3:
\[
v = 14.
\]
This means that the two plans will cost the same amount when Leila makes 14 visits.
Now, let’s analyze the options given:
1. **Plan X costs $5 per visit. Plan Y costs $42 per month and $2 per visit.**
- Cost for Plan X for \(v\) visits: \(5v\)
- Cost for Plan Y for \(v\) visits: \(42 + 2v\)
- Setting them equal gives \(5v = 42 + 2v\).
- This matches our equation.
2. **Plan X costs $5 per visit. Plan Y costs $2 per month and $42 per visit.**
- Cost for Plan X for \(v\) visits: \(5v\)
- Cost for Plan Y for \(v\) visits: \(2 + 42v\), which would not lead to our equation.
3. **Plan X costs $5 per month. Plan Y costs $42 per month and $2 per visit.**
- Cost for Plan X for \(v\) visits: \(5\)
- Cost for Plan Y for \(v\) visits: \(42 + 2v\), which doesn't fit.
4. **Plan X costs $5 per month. Plan Y costs $2 per month and $42 per visit.**
- Cost for Plan X for \(v\) visits: \(5\) (doesn’t change with visits)
- Cost for Plan Y for \(v\) visits: \(2 + 42v\), which isn't what we need.
5. **Plan X costs $5 per visit plus $42 per month. Plan Y costs $2 per visit plus $42 per month.**
- Cost for Plan X: \(5v + 42\)
- Cost for Plan Y: \(2v + 42\)
- Setting them equal gives \(5v + 42 = 2v + 42\), which does not match either.
The correct option is:
**Plan X costs $5 per visit. Plan Y costs $42 per month and $2 per visit. How many visits, v, would Leila need to make per month for these options to be equal in price?**
The equation can be rearranged as follows:
1. Start with the original equation: \(5v = 2v + 42\).
2. Subtract \(2v\) from both sides:
\[
5v - 2v = 42 \implies 3v = 42.
\]
3. Divide both sides by 3:
\[
v = 14.
\]
This means that the two plans will cost the same amount when Leila makes 14 visits.
Now, let’s analyze the options given:
1. **Plan X costs $5 per visit. Plan Y costs $42 per month and $2 per visit.**
- Cost for Plan X for \(v\) visits: \(5v\)
- Cost for Plan Y for \(v\) visits: \(42 + 2v\)
- Setting them equal gives \(5v = 42 + 2v\).
- This matches our equation.
2. **Plan X costs $5 per visit. Plan Y costs $2 per month and $42 per visit.**
- Cost for Plan X for \(v\) visits: \(5v\)
- Cost for Plan Y for \(v\) visits: \(2 + 42v\), which would not lead to our equation.
3. **Plan X costs $5 per month. Plan Y costs $42 per month and $2 per visit.**
- Cost for Plan X for \(v\) visits: \(5\)
- Cost for Plan Y for \(v\) visits: \(42 + 2v\), which doesn't fit.
4. **Plan X costs $5 per month. Plan Y costs $2 per month and $42 per visit.**
- Cost for Plan X for \(v\) visits: \(5\) (doesn’t change with visits)
- Cost for Plan Y for \(v\) visits: \(2 + 42v\), which isn't what we need.
5. **Plan X costs $5 per visit plus $42 per month. Plan Y costs $2 per visit plus $42 per month.**
- Cost for Plan X: \(5v + 42\)
- Cost for Plan Y: \(2v + 42\)
- Setting them equal gives \(5v + 42 = 2v + 42\), which does not match either.
The correct option is:
**Plan X costs $5 per visit. Plan Y costs $42 per month and $2 per visit. How many visits, v, would Leila need to make per month for these options to be equal in price?**