A gym offers two membership options: basic and premium. A basic membership costs $30 per month, and a premium membership costs $50 per month. If the gym has 40 members and collects $1,500 in membership fees, what system of equations represents the situation?
A. $30x+50y=40, x+y=1500$
B. $50x+30y=40, x+y=1500$
C. $50x+30y=1500, x+y=40$
D. $30x+50y=1500, x+y=40

Question

GinnyAnswer · Answer

Define variables: Let x be the number of basic memberships and y be the number of premium memberships. 
 Write the equation for the total number of members: x + y = 40 . 
 Write the equation for the total membership fees: 30 x + 50 y = 1500 . 
 The system of equations is x + y = 40 and 30 x + 50 y = 1500 , which corresponds to option d. d ​ 
 
 Explanation 
 
 Define variables and write the first equation Let x be the number of basic memberships and y be the number of premium memberships. The total number of members is 40, so we have the equation 
 
 First equation x + y = 40 
 
 Write the second equation based on the fees The total membership fees collected is $1500 . Since basic memberships cost $30 and premium memberships cost $50 , we have the equation 
 
 Second equation 30 x + 50 y = 1500 
 
 System of equations Therefore, the system of equations that represents the situation is 
 
 Final Answer x + y = 40 30 x + 50 y = 1500 This corresponds to option d.

Examples 
 Imagine you're organizing a school event and need to figure out how many tickets to sell at different prices to reach a fundraising goal. This problem is similar to figuring out how many basic and premium gym memberships there are, given the total number of members and the total revenue. By setting up a system of equations, you can determine the exact number of tickets needed at each price point to meet your financial target. This method is also useful in budgeting, resource allocation, and even in planning investment strategies where you have different investment options with varying returns.

Anonymous · Answer

The system of equations for this gym membership problem is defined by the equations x + y = 40 (for total members) and 30 x + 50 y = 1500 (for membership fees). Therefore, the correct option is D. 
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Answer (2)

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