Tickets for a concert were $5 for each child and $8 for each adult. At one of the concerts, each adult brought 4 children with them, and 10 children attended without an adult. The total ticket sales were $1,730. Which of the following systems of equations can be solved to determine the number of children, c, and adults, a, who attended the concert? Choose 1 answer: (A) 5c+8a=1,730 4a+10=c (B) 5c+8a=1,730 4a-10=c (C) 8c+5a=1,730 4a+10=c (D) 8c+5a=1,730 4a-10=c

Question

Tickets for a concert were  $5 for each child and  $8 for each adult. At one of the concerts, each adult brought 4 children with them, and 10 children attended without an adult. The total ticket sales were  $1,730. Which of the following systems of equations can be solved to determine the number of children,  c, and adults,  a, who attended the concert? Choose 1 answer: (A)  5c+8a=1,730  4a+10=c (B)  5c+8a=1,730  4a-10=c (C)  8c+5a=1,730  4a+10=c (D)  8c+5a=1,730  4a-10=c

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Translate into mathematical expressions: Translate the given information into mathematical expressions. We know that each child's ticket costs $5 and each adult's ticket costs $8. The total sales from tickets are $1,730. We also know that for each adult, there are 4 children, and there are 10 additional children who attended without an adult. We can represent the number of children as c and the number of adults as a.Set up first equation: Set up the first equation based on the total ticket sales. The total amount from children's tickets is 5c (since each child's ticket is $5) and from adults' tickets is 8a (since each adult's ticket is $8). The total sales are $1,730, so the first equation is: 5c + 8a = 1,730Set up second equation: Set up the second equation based on the relationship between the number of children and adults. Each adult brings 4 children, so the number of children brought by adults is 4a. There are also 10 additional children who came without an adult. Therefore, the total number of children is the sum of children brought by adults and the children who came alone: c = 4a + 10Identify correct system: Identify the correct system of equations from the given options. We have two equations from the previous steps: 1. 5c + 8a = 1,730 (Total ticket sales) 2. c = 4a + 10 (Relationship between children and adults) Now we need to match these equations with the given options. The correct system of equations that matches our derived equations is: (A) 5c + 8a = 1,730     4a + 10 = c

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