A tile factory earns money by charging a flat fee for delivery and a sales price of $0.25 per tile. One customer paid a sum for 10,000 tiles. The equation [tex]y-3,000=0.25(x-10,000)[/tex] models the revenue of the the factory, where [tex]x[/tex] is the number of tiles and [tex]y[/tex] is the total cost to the customer.
Which function describes the revenue of the tile factory in terms of tiles sold?
What is the flat fee for delivery?
Answer (2)
Rewrite the given equation y − 3000 = 0.25 ( x − 10000 ) .
Distribute 0.25 to get y − 3000 = 0.25 x − 2500 .
Isolate y to find the revenue function: y = 0.25 x + 500 .
The flat fee for delivery is 500 .
Explanation
Understanding the Problem Let's analyze the problem. We are given the equation y − 3000 = 0.25 ( x − 10000 ) which models the revenue of the tile factory. Here, x represents the number of tiles sold, and y represents the total cost to the customer. We need to find the revenue function in terms of tiles sold and the flat fee for delivery.
Rewriting the Equation First, we need to rewrite the given equation in the slope-intercept form, which is y = m x + b , where m is the slope (price per tile) and b is the y-intercept (flat fee).
Given Equation Starting with the given equation: y − 3000 = 0.25 ( x − 10000 )
Distributing Distribute the 0.25 on the right side: y − 3000 = 0.25 x − 0.25 ( 10000 ) y − 3000 = 0.25 x − 2500
Isolating y Add 3000 to both sides to isolate y :
y = 0.25 x − 2500 + 3000 y = 0.25 x + 500
Finding the Flat Fee So, the revenue function is y = 0.25 x + 500 . This means the flat fee for delivery is $500.
Final Answer Therefore, the function that describes the revenue of the tile factory in terms of tiles sold is y = 0.25 x + 500 , and the flat fee for delivery is $500 .
Examples
Understanding revenue models is crucial in business. For instance, a streaming service might charge a subscription fee plus an additional cost for premium content. If their revenue model is represented by y = 5 x + 100 , where x is the number of premium contents accessed and y is the total revenue, this model helps them predict income based on user activity and adjust pricing strategies accordingly. This kind of analysis helps in making informed decisions about pricing and service offerings.
The function describing the revenue of the tile factory in terms of tiles sold is y = 0.25 x + 500 , where $0.25$ is the price per tile. The flat fee for delivery is $500.
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