Liz won a bunch of tickets at the arcade. She plans to spend most of them on one large item and use the rest to buy hair ties. An employee at the arcade tells Liz that if she buys the kickball for 2,200 tickets, she will have exactly enough left for 13 hair ties. However, if she buys the toy airplane for 2,500 tickets, she will have exactly enough left for 7 hair ties. Which equation can you use to find t, the number of tickets Liz needs for each hair tie? Choices: (A)2,200 + 13t = 2,500 - 7t (B)2,200 + 13t = 2,500 + 7t How many tickets does Liz need for each hair tie? ____ tickets

Question

Liz won a bunch of tickets at the arcade. She plans to spend most of them on one large item and use the rest to buy hair ties. An employee at the arcade tells Liz that if she buys the kickball for 2,200 tickets, she will have exactly enough left for 13 hair ties. However, if she buys the toy airplane for 2,500 tickets, she will have exactly enough left for 7 hair ties. Which equation can you use to find t, the number of tickets Liz needs for each hair tie?   Choices: (A)2,200 + 13t = 2,500 - 7t (B)2,200 + 13t = 2,500 + 7t  How many tickets does Liz need for each hair tie?   ____ tickets

Bytelearn · Accepted Answer

Define Variables: Let's denote the total number of tickets Liz has by T and the number of tickets needed for each hair tie by t. According to the problem, if Liz buys the kickball, she will spend 2,200 tickets and have enough left for 13 hair ties. This can be represented by the equation T - 2,200 = 13t. Similarly, if she buys the toy airplane, she will spend 2,500 tickets and have enough left for 7 hair ties, which can be represented by the equation T - 2,500 = 7t. Since the total number of tickets T is the same in both scenarios, we can set the two expressions for the remaining tickets equal to each other to find the value of t.Set Up Equations: Set up the equation based on the information given: 2,200 + 13t = T and 2,500 + 7t = T. Since both expressions are equal to T, we can set them equal to each other: 2,200 + 13t = 2,500 + 7t.Solve for t: To solve for t, we need to get all the terms with t on one side and the constants on the other. Subtract 7t from both sides: 2,200 + 13t - 7t = 2,500 + 7t - 7t. This simplifies to 2,200 + 6t = 2,500.Isolate t Term: Now, subtract 2,200 from both sides to isolate the term with t: 2,200 + 6t - 2,200 = 2,500 - 2,200. This simplifies to 6t = 300.Final Solution: Finally, divide both sides by 6 to solve for t: 6t / 6 = 300 / 6. This gives us t = 50.

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