Gavin has a points card for a movie theater.
He receives 20 rewards points just for signing up.
He earns 9.5 points for each visit to the movie theater.
He needs 77 points for a free movie ticket.

Which equation could be used to determine vv, the number of visits Gavin must make to earn a free movie ticket?
Answer
Multiple Choice Answers
start fraction, 7, 7, minus, 20, divided by, 9, point, 5, end fraction, equals, v 
9.5 
2
1
​
 
2
1
​
 
​
 
77−20
​
 =v
77, equals, 9, point, 5, left parenthesis, 20, plus, v, right parenthesis77=9.5(20+v)
9, point, 5, v, equals, 20, minus, 779.5v=20−77
20, v, equals, 77, minus, 9, point, 520v=77−9.5Gavin has a points card for a movie theater.
He receives 20 rewards points just for signing up.
He earns 9.5 points for each visit to the movie theater.
He needs 77 points for a free movie ticket.

Which equation could be used to determine vv, the number of visits Gavin must make to earn a free movie ticket?
Answer
Multiple Choice Answers
start fraction, 7, 7, minus, 20, divided by, 9, point, 5, end fraction, equals, v 
9.5 
2
1
​
 
2
1
​
 
​
 
77−20
​
 =v
77, equals, 9, point, 5, left parenthesis, 20, plus, v, right parenthesis77=9.5(20+v)
9, point, 5, v, equals, 20, minus, 779.5v=20−77
20, v, equals, 77, minus, 9, point, 520v=77−9.5

To determine the correct equation that represents the number of visits, \( v \), Gavin needs to earn a free movie ticket, let's break down the problem step by step:

1. **Initial Points**: Gavin starts with 20 points just for signing up.
2. **Points per Visit**: For each visit to the theater, he earns 9.5 points.
3. **Target Points**: He needs 77 points for a free movie ticket.

### General Equation:
The total points Gavin earns can be expressed as:

\[
\text{Total points} = 20 + 9.5v
\]

Where:
- \( 20 \) is the points he gets for signing up.
- \( 9.5v \) is the points he earns for \( v \) visits.

We want to know how many visits \( v \) he needs to reach 77 points. So we set the total points equal to 77:

\[
20 + 9.5v = 77
\]

### Solving for \( v \):
Subtract 20 from both sides:

\[
9.5v = 77 - 20
\]

\[
9.5v = 57
\]

Now divide by 9.5:

\[
v = \frac{57}{9.5}
\]

So the correct equation to find \( v \) is:

\[
\frac{77 - 20}{9.5} = v
\]

### Answer:
This matches the first option:

\[
\frac{77 - 20}{9.5} = v
\]

Would you like more details or have any questions?

Here are 5 related questions you can consider:
1. How many visits would Gavin need if the points per visit increased to 10 points?
2. What if Gavin had started with 50 points instead of 20? How would that change the equation?
3. If Gavin wanted to save up for two free tickets, how many visits would he need?
4. How would the number of visits change if the required points for a free movie ticket increased to 100?
5. How many points would Gavin earn after 5 visits?

**Tip**: When solving word problems, always define the variables clearly and translate the word problem into an equation before solving!

Gavin has a points card for a movie theater. He receives 20 rewards points just for signing up. He earns 9.5 points for each visit to the movie theater. He needs 77 points for a free movie ticket. Which equation could be used to determine v, the number of visits Gavin must make to earn a free movie ticket?

Explore how to solve a linear equation to determine the number of visits Gavin must make to earn a free movie ticket. Learn how starting points, points per visit, and target points contribute to the solution. Suitable for students in Grades 6-8.

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