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

Question

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

GinnyAnswer · Answer

Define the variable: Let x represent the number of video games rented. 
 Formulate the equation: The total cost is the sum of the movie rental and the cost of the video games: 4 + 6 x = 22 . 
 Solve for x : Subtract 4 from both sides and then divide by 6 to find x = 3 . 
 State the answer: Marcus rented 3 ​ video games and the equation is 4 + 6 x = 22 . 
 
 Explanation 
 
 Problem Analysis Let's analyze the problem. Marcus rented a movie for $4 and some video games for $6 each. He paid a total of $22. We need to find the equation that models this situation and the number of video games he rented. 
 
 Forming 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 video games is 6 x . The total cost is the sum of the cost of the movie and the cost of the video games, which is 4 + 6 x . We know that the total cost is $22, so we can write the equation as: 4 + 6 x = 22 
 
 Solving for x Now, let's solve the equation for x . Subtract 4 from both sides of the equation: 4 + 6 x − 4 = 22 − 4 
 6 x = 18 
 
 Finding the Number of Games Divide both sides by 6: 6 6 x ​ = 6 18 ​ 
 x = 3 
So, Marcus rented 3 video games. 
 
 Final Answer The equation that models the situation is 4 + 6 x = 22 , and the number of video games Marcus rented is 3. Therefore, the correct choices are A and D.

Examples 
 Imagine you are organizing a birthday party and have a budget of $50. You want to buy a cake for $20 and some party favors that cost $5 each. This problem helps you determine how many party favors you can buy without exceeding your budget. By setting up an equation similar to the one in the problem, you can calculate the maximum number of party favors you can purchase, ensuring you stay within your budget and make the party a success. This type of problem demonstrates how algebraic equations can be used to manage expenses and make informed decisions in everyday situations.

Answer (1)

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