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=2,500−7tHow many tickets does Liz need for each hair tie?____ tickets
Q. 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=2,500−7tHow many tickets does Liz need for each hair tie?____ tickets
Equation Setup: 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.
Isolate Variable: Set up the equation based on the information given: 2,200+13t=2,500+7t. This equation represents the fact that the remaining tickets after buying either the kickball or the toy airplane are used to buy hair ties, and the cost in tickets for the hair ties is the same in both scenarios.
Simplify Equation: To solve for t, we need to isolate the variable on one side of the equation. We can do this by subtracting 7t from both sides of the equation to get the t terms on one side: 2,200+13t−7t=2,500+7t−7t.
Subtract Terms: Simplify the equation: 2,200+6t=2,500. This simplification combines like terms by subtracting 7t from both sides.
Divide and Calculate: Now, subtract 2,200 from both sides of the equation to isolate the term with t: 2,200+6t−2,200=2,500−2,200.
Divide and Calculate: Now, subtract 2,200 from both sides of the equation to isolate the term with t: 2,200+6t−2,200=2,500−2,200. Simplify the equation again: 6t=300. This step involves performing the subtraction on both sides of the equation.
Divide and Calculate: Now, subtract 2,200 from both sides of the equation to isolate the term with t: 2,200+6t−2,200=2,500−2,200. Simplify the equation again: 6t=300. This step involves performing the subtraction on both sides of the equation. Finally, divide both sides of the equation by 6 to solve for t: 66t=6300.
Divide and Calculate: Now, subtract 2,200 from both sides of the equation to isolate the term with t: 2,200+6t−2,200=2,500−2,200.Simplify the equation again: 6t=300. This step involves performing the subtraction on both sides of the equation.Finally, divide both sides of the equation by 6 to solve for t: 6t/6=300/6.Calculate the value of t: t=50. This is the number of tickets Liz needs for each hair tie.
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