1. For the Summer R&B/Soul Festival, there is one price for students, one for adults, and another for senior citizens. The Jackson family bought 3 student tickets and 2 adult tickets for $104. The Williams family bought 5 student tickets, 1 adult ticket, and 2 senior citizen tickets for $155. The Mullins family bought 2 of each for $126. a. Write a system of equations that can be used to find the cost of each ticket. b. Solve the system by elimination to find the cost of each ticket.
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Question:
1. For the Summer R&B/Soul Festival, there is one price for students, one for adults, and another for senior citizens. The Jackson family bought 3 student tickets and 2 adult tickets for $104. The Williams family bought 5 student tickets, 1 adult ticket, and 2 senior citizen tickets for $155. The Mullins family bought 2 of each for $126. a. Write a system of equations that can be used to find the cost of each ticket. b. Solve the system by elimination to find the cost of each ticket.
Answers
Answer:Step-by-step explanation:Let's call student tickets s, adult tickets a and senior tickets c. The equations for each family are as follows:Jackson: 3s + 2a = 104Williams: 5s + 1a + 2c = 155Mullins: 2s + 2a + 2c = 126To get started, let's solve the Jackson family equation for a:2a = 104 - 3s soa = 52 - 1.5sNow we can use that a value in the Williams equation:5s + 1(52 - 1.5s) + 2c = 155 and5s + 52 - 1.5s + 2c = 155 and3.5s + 2c = 103We can also use that a value in the Mullins equation:2s + 2(52 - 1.5s) + 2c = 126 and2s + 104 - 3s + 2c = 126 so-1s + 2c = 22Solve the system that is in bold print now by multiplying the Mullins equation through by -1 to get a new system that looks like this: 3.5s + 2c = 103 1s - 2c = -22The c's eliminate each other leaving us with only s's:4.5s = 81 sos = 18The cost of a student ticket is $18. Now use that $18 in place of s in the first bold equation above:3.5(18) + 2c = 103 and63 + 2c = 103 and2c = 40 soc = 20The cost of a senor ticket is $20. Now use both of those values in the Williams equation at the beginning to solve for a:5(18) + 1a + 2(20) = 155 and90 + 1a + 40 = 155 and1a = 25The cost of an adult ticket is $25
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