Select the correct answer.
The concession stand at the high school football stadium sells hot dogs and hamburgers to raise money for the high school athletic programs. Each hot dog sold earns the programs $0.50, and each hamburger sold earns $0.75. This week, the concession stand sold a combination of 230 hot dogs and hamburgers and earned $138.50 for the athletic programs. If $x$ represents the number of hot dogs sold and $y$ represents the number of hamburgers sold, which system of equations represents this situation?
A. $0.75 x+0.50 y=230$
$x+y=138.50$
B. $0.50 x+0.75 y=138.50$
$x+y=230$
C. $0.75 x+0.50 y=138.50$
$x+y=230$
D. $0.50 x+0.75 y=230$
$x+y=138.50
Answer (2)
The correct system of equations for the concession stand scenario is represented by Option B, which is: 0.50 x + 0.75 y = 138.50 and x + y = 230. This accurately reflects both the total number of items sold and the total earnings. Therefore, the final answer is B.
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Set up an equation for the total number of items sold: x + y = 230 .
Set up an equation for the total earnings: 0.50 x + 0.75 y = 138.50 .
Combine the two equations to form a system of equations.
The correct system of equations is: 0.50 x + 0.75 y = 138.50 x + y = 230 .
Explanation
Problem Analysis Let's analyze the problem. We are given that the concession stand sells hot dogs and hamburgers. Each hot dog earns $0.50 and each hamburger earns $0.75 . This week, 230 hot dogs and hamburgers were sold, and the total earnings were $138.50 . We need to find the system of equations that represents this situation, where x is the number of hot dogs and y is the number of hamburgers sold.
Equation Setup We can set up two equations based on the given information. The first equation represents the total number of hot dogs and hamburgers sold, which is 230. So, we have: x + y = 230 The second equation represents the total earnings from selling hot dogs and hamburgers, which is $138.50 . Since each hot dog earns $0.50 and each hamburger earns $0.75 , we have: 0.50 x + 0.75 y = 138.50
System of Equations Now we have the system of equations: x + y = 230 0.50 x + 0.75 y = 138.50 We need to find the option that matches this system of equations.
Finding the Correct Option Comparing our system of equations with the given options: A. 0.75 x + 0.50 y = 230 x + y = 138.50 B. 0.50 x + 0.75 y = 138.50 x + y = 230 C. 0.75 x + 0.50 y = 138.50 x + y = 230 D. 0.50 x + 0.75 y = 230 x + y = 138.50 Option B matches our system of equations.
Final Answer Therefore, the correct answer is option B.
Examples
This type of problem is useful in business when you need to determine the number of items sold based on the total revenue and the price of each item. For example, a store sells two types of products, and you know the price of each product, the total number of products sold, and the total revenue. You can use a system of equations to find out how many of each product were sold. This helps in inventory management and understanding sales patterns.
