Marcus rented a movie for $4 and some video games for $6 each. He paid $22. How many games did he rent?
Choose two answers: one for the equation that models this situation and one for the correct answer.
A. Equation: [tex]4+6 x=22[/tex]
B. Equation: [tex]6+4 x=22[/tex]
C. Answer: 4 video games
D. Answer: 3 video games
Answer (2)
Define x as the number of video games rented.
Formulate the equation: 4 + 6 x = 22 .
Solve for x : x = 6 18 = 3 .
Marcus rented 3 video games.
Explanation
Problem Analysis Let's analyze the problem. Marcus rented a movie for $4 and some video games for $6 each. He paid $22 in total. We need to find the number of video games he rented and the equation that represents this situation.
Formulating the Equation Let x be the number of video games Marcus rented. The cost of the movie is $4, and the cost of the video games is $6 per game, so the total cost for the games is 6 x . The total amount Marcus paid is $22. Therefore, the equation that models this situation is: 4 + 6 x = 22
Solving the Equation Now, let's solve the equation for x :
4 + 6 x = 22 Subtract 4 from both sides of the equation: 6 x = 22 − 4 6 x = 18 Divide both sides by 6: x = 6 18 x = 3
Final Answer So, Marcus rented 3 video games. The equation that models the situation is 4 + 6 x = 22 , and the number of video games he rented is 3.
Examples
Imagine you're organizing a school event. You have a fixed cost for renting the venue, and a variable cost for each student attending. This problem is similar to figuring out how many students can attend the event given your budget, the venue cost, and the cost per student. Understanding how to set up and solve these equations helps in budgeting and planning events effectively. For example, if the venue costs $100 and each student costs $10, and you have a budget of $500, you can determine how many students can attend.
The equation that models the situation is 4 + 6 x = 22 , and Marcus rented 3 video games. Therefore, the correct options are A for the equation and D for the answer.
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