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Question

Jose has a points card for a movie theater. He receives 50 rewards points just for signing up. He earns 3.5 points for each visit to the movie theater. He needs at least 85 points for a free movie ticket. Write and solve an inequality which can be used to determine æ, the number of visits Jose can make to earn his first free movie ticket.SHOW LESS73

Solution

user avatar imageAnswer\(x \geqslant 10\)ExplanationStep 1: Let \(x\) represent the number of visits Jose needs to make to earn at least 85 points. Step 2: Write the inequality representing the total points Jose can earn after \(x\) visits, which includes the initial 50 points for signing up: \(50 + 3.5x \geqslant 85\). Step 3: Subtract 50 from both sides of the inequality to isolate the term with \(x\): \(3.5x \geqslant 85 - 50\). Step 4: Simplify the right side of the inequality: \(3.5x \geqslant 35\). Step 5: Divide both sides of the inequality by 3.5 to solve for \(x\): \(x \geqslant \frac{35}{3.5}\). Step 6: Calculate the value of \(x\): \(x \geqslant 10\). Therefore, Jose needs to make at least 10 visits to earn his first free movie ticket.Click to rate:35.5(93 votes)Search questionBy textBy image/screenshotDrop your file here orClick Hereto upload

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