Question

ryan has a points card for a movie theater.

• he receives 85 rewards points just for signing up.
• he earns 7.5 points for each visit to the movie theater.
• he needs 160 points for a free movie ticket.

write and solve an equation which can be used to determine v, the number of visits ryan must make to earn a free movie ticket.
answer attempt 1 out of 3
equation:
answer: v =

Explanation:

Step1: Define the equation structure

The total points Ryan has is the sign - up points plus the points from each visit. The sign - up points are 85, and for each of the \(v\) visits, he gets 7.5 points. He needs 160 points for a free ticket. So the equation is \(85 + 7.5v=160\).

Step2: Solve for \(v\)

Subtract 85 from both sides of the equation:
\(7.5v=160 - 85\)
\(7.5v = 75\)
Then divide both sides by 7.5:
\(v=\frac{75}{7.5}\)
\(v = 10\)

Answer:

Equation: \(85 + 7.5v=160\)