A school is selling two types of tickets for a play: student tickets and adult tickets. Student tickets cost $5, and adult tickets cost $10. If 200 tickets are sold and the total revenue is $1,500, what system of equations represents the situation?
a. $5x+10y=200, x+y=1500$
b. $10x+5y=1500, x+y=200$
c. $5x+10y=1500, x+y=200$
d. $10x+5y=200, x+y=1500

Question

GinnyAnswer · Answer

Define variables: Let x be the number of student tickets and y be the number of adult tickets. 
 Write the equation for the total number of tickets: x + y = 200 . 
 Write the equation for the total revenue: 5 x + 10 y = 1500 . 
 The system of equations is x + y = 200 and 5 x + 10 y = 1500 , which corresponds to option c: 5 x + 10 y = 1500 , x + y = 200 ​ . 
 
 Explanation 
 
 Define variables and write first equation Let x be the number of student tickets sold and y be the number of adult tickets sold. We know that the total number of tickets sold is 200, so we can write the equation: 
 
 First equation x + y = 200 
 
 Write second equation based on revenue We also know that student tickets cost $5 and adult tickets cost $10 , and the total revenue is $1500 . So we can write the equation: 
 
 Second equation 5 x + 10 y = 1500 
 
 System of equations Therefore, the system of equations that represents the situation is: 
 
 First equation x + y = 200 
 
 Second equation 5 x + 10 y = 1500 
 
 Find the correct option Comparing this system of equations with the given options, we see that option c matches our system of equations. 
 
 Final Answer The correct answer is c. 5 x + 10 y = 1500 , x + y = 200

Examples 
 Imagine you are organizing a bake sale to raise money for your school club. You are selling cookies for $2 each and brownies for $3 each. If you sell a total of 50 items and raise $120 , you can use a system of equations to determine how many cookies and brownies you sold. This helps in managing inventory and tracking sales in real-world scenarios.

Anonymous · Answer

The system of equations representing the ticket sales situation is 5 x + 10 y = 1500 and x + y = 200 . This corresponds to option c. I have confirmed the accuracy of these equations based on the details given in the problem. 
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Answer (2)

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