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- He receives 70 rewards points just for signing up. He earns 9.5 points for each visit to the movie theater. He needs 184 points for a free movie ticket. Write and solve an equation which can be used to determine \( v \), the number of visits Marques must make to earn a free movie ticket. Answer Attempt t out of 2 Equation: Answer: \( v=\square \)

Ask by Fernandez Turner. in the United States
Mar 13,2025

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To find the number of visits \( v \) Marques needs to make to earn 184 points, use the equation: \[ 70 + 9.5v = 184 \] Solving for \( v \): \[ 9.5v = 184 - 70 \] \[ 9.5v = 114 \] \[ v = \frac{114}{9.5} \] \[ v = 12 \] So, Marques must make **12 visits** to earn a free movie ticket.

Solución

Let's denote the number of visits Marques must make to earn a free movie ticket as \( v \). Given: - He receives 70 rewards points just for signing up. - He earns 9.5 points for each visit to the movie theater. - He needs 184 points for a free movie ticket. The total points Marques needs to earn for a free movie ticket is the sum of the points he receives for signing up and the points he earns for each visit to the movie theater. This can be represented by the equation: \[ 70 + 9.5v = 184 \] Now, we can solve this equation to find the value of \( v \), the number of visits Marques must make to earn a free movie ticket. Solve the equation by following steps: - step0: Solve for \(v\): \(70+9.5v=184\) - step1: Move the constant to the right side: \(9.5v=184-70\) - step2: Subtract the numbers: \(9.5v=114\) - step3: Divide both sides: \(\frac{9.5v}{9.5}=\frac{114}{9.5}\) - step4: Divide the numbers: \(v=12\)

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The Deep Dive

To determine how many visits Marques needs to make, we can set up the equation based on the rewards points he receives. Since he gets 70 points for signing up and earns 9.5 points for each visit, we can express this as: \[ 70 + 9.5v = 184 \] Now, we can solve for \( v \): 1. Subtract 70 from both sides: \( 9.5v = 184 - 70 \) \( 9.5v = 114 \) 2. Divide both sides by 9.5: \( v = \frac{114}{9.5} \) \( v \approx 12 \) So, Marques must make approximately 12 visits to earn enough points for a free movie ticket!

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