Thomas was selling tickets to his school play. The tickets cost $[tex]$5.00$[/tex] for adults and $[tex]$2.00$[/tex] for children. He sold 200 tickets and collected $[tex]$610$[/tex]. Which system represents the number of adult and child tickets that Thomas sold?

[tex]
\begin{array}{r}
x+y=200 \
5 x+2 y=610
\end{array}
[/tex]

[tex]$x+y=610$
$5 x+2 y=200$[/tex]

[tex]
\begin{array}{r}
x+y=200 \
x+2 y=610
\end{array}
[/tex]

[tex]$x+y=200$
$5 x+y=610$[/tex]

Question

Thomas was selling tickets to his school play. The tickets cost $[tex]$5.00$[/tex] for adults and $[tex]$2.00$[/tex] for children. He sold 200 tickets and collected $[tex]$610$[/tex]. Which system represents the number of adult and child tickets that Thomas sold?

[tex]
\begin{array}{r}
x+y=200 \
5 x+2 y=610
\end{array}
[/tex]

[tex]$x+y=610$
$5 x+2 y=200$[/tex]

[tex]
\begin{array}{r}
x+y=200 \
x+2 y=610
\end{array}
[/tex]

[tex]$x+y=200$
$5 x+y=610$[/tex]

Anonymous · Answer

The system of equations representing the number of adult and child tickets Thomas sold is { x + y = 200 5 x + 2 y = 610 ​ . This matches the first option provided in the question. Therefore, the chosen option is the first one. 
 ;

GinnyAnswer · Answer

Define variables: Let x be the number of adult tickets and y be the number of child tickets. 
 Write the equation for the total number of tickets: x + y = 200 . 
 Write the equation for the total amount collected: 5 x + 2 y = 610 . 
 The system of equations is: { x + y = 200 5 x + 2 y = 610 ​ , which matches the first option. x + y = 200 5 x + 2 y = 610 ​ ​ 
 
 Explanation 
 
 Problem Analysis Let's analyze the problem. We are given that Thomas sold tickets to a school play. Adult tickets cost $5.00 and children's tickets cost $2.00. He sold a total of 200 tickets and collected $610. We need to find the system of equations that represents the number of adult and child tickets sold. 
 
 Equation for Total Tickets Let x be the number of adult tickets sold and y be the number of child tickets sold. The total number of tickets sold is 200, so we have the equation: x + y = 200 
 
 Equation for Total Amount Collected The total amount collected is $610. The amount collected from adult tickets is 5 x and the amount collected from child tickets is 2 y . So we have the equation: 5 x + 2 y = 610 
 
 System of Equations Therefore, the system of equations that represents the number of adult and child tickets sold is: { x + y = 200 5 x + 2 y = 610 ​ 
 
 Matching the System of Equations Comparing this system of equations with the given options, we see that the first option matches our system of equations.

Examples 
 Imagine you're organizing a bake sale. You sell cookies for $1 and brownies for $2. You want to sell 50 items in total and make $75. Setting up a system of equations like this helps you figure out exactly how many cookies and brownies you need to bake! This is a practical way to use algebra to solve everyday problems.

Answer (2)

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