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A tile factory earns money by charging a flat fee for delivery and a sales price of [tex]$0.25 per tile. One customer paid a total of $[/tex]3,000 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?

2. What is the flat fee for delivery?
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Answer :

GinnyAnswer
To find the flat fee for delivery, we need to determine the value in the provided equation [tex]\(y - 3000 = 0.25(x - 10000)\)[/tex]. This equation describes the relationship between the total cost [tex]\(y\)[/tex] and the number of tiles [tex]\(x\)[/tex] sold.

First, rewrite the equation in the form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the cost per tile and [tex]\(b\)[/tex] is the flat fee. Let’s start by expanding and rearranging the given equation:

1. Starting with the given equation:

[tex]\[ y - 3000 = 0.25(x - 10000) \][/tex]

2. Distribute the [tex]\(0.25\)[/tex]:

[tex]\[ y - 3000 = 0.25x - 0.25 \times 10000 \][/tex]

[tex]\[ y - 3000 = 0.25x - 2500 \][/tex]

3. Add [tex]\(3000\)[/tex] to both sides to isolate [tex]\(y\)[/tex]:

[tex]\[ y = 0.25x - 2500 + 3000 \][/tex]

4. Combine the constant terms:

[tex]\[ y = 0.25x + 500 \][/tex]

So, the function that describes the revenue [tex]\(y\)[/tex] of the tile factory in terms of [tex]\(x\)[/tex] tiles sold is:

[tex]\[ y = 0.25x + 500 \][/tex]

From this equation, we can directly see the flat fee for delivery in the constant term.

Therefore, the flat fee for delivery is:

[tex]\[ \$ 500 \][/tex]

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