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A tile factory earns money by charging a flat fee for delivery and a sales price of [tex]\$0.25[/tex] per tile. One customer paid a total of [tex]\$3,000[/tex] for 10,000 tiles. The equation [tex]y - 3,000 = 0.25(x - 10,000)[/tex] models the revenue of the tile factory, where [tex]x[/tex] is the number of tiles and [tex]y[/tex] is the total cost to the customer.

1. Which function describes the revenue of the tile factory in terms of tiles sold?
[tex]\square[/tex]

2. What is the flat fee for delivery?
[tex]\$ \square[/tex]



Answer :

GinnyAnswer
To determine the revenue function and the flat fee for delivery, we start with the given equation:
[tex]\[ y - 3000 = 0.25(x - 10000) \][/tex]

1. Simplify the given equation to get the revenue function:

Begin by distributing the [tex]$0.25$[/tex] on the right-hand side:
[tex]\[ y - 3000 = 0.25x - 2500 \][/tex]

Next, isolate [tex]$y$[/tex] by adding [tex]$3000$[/tex] to both sides of the equation:
[tex]\[ y = 0.25x - 2500 + 3000 \][/tex]

Simplify the right-hand side:
[tex]\[ y = 0.25x + 500 \][/tex]

Thus, the revenue function in terms of the number of tiles sold ([tex]$x$[/tex]) is:
[tex]\[ y = 0.25x + 500 \][/tex]

2. Identify the flat fee for delivery:

The flat fee for delivery is the constant term in the revenue function (the term that does not depend on [tex]$x$[/tex]). In the revenue function [tex]$y = 0.25x + 500$[/tex], the term [tex]$500$[/tex] represents the flat fee for delivery.

Therefore,

- The function that describes the revenue of the tile factory in terms of tiles sold is:
[tex]\[ y = 0.25x + 500 \][/tex]

- The flat fee for delivery is:
[tex]\[ \$500 \][/tex]

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