You Want To Order Posters To Advertise Your Band. A Company Charges $ 109.95 \$109.95 $109.95 For The First 100 Posters And $ 65 \$65 $65 For Each Additional 100 Posters.a. Write The Equation That Represents The Total Cost Y Y Y (in Dollars) As A

You Want to Order Posters to Advertise Your Band: A Cost Analysis

As a band, promoting your music and upcoming events is crucial to attracting new fans and increasing your popularity. One effective way to do this is by ordering posters to display in local music stores, coffee shops, and other public areas. However, the cost of ordering posters can add up quickly, especially if you need a large quantity. In this article, we will explore the cost of ordering posters from a company that charges a base fee for the first 100 posters and a lower fee for each additional 100 posters.

Let's assume that the company charges $\$109.95$ for the first 100 posters and $\$65$ for each additional 100 posters. If you order $x$ posters, the total cost $y$ (in dollars) can be represented by the following equation:

$$y = 109.95 + 65 \left( \frac{x - 100}{100} \right)$$

To simplify the equation, we can start by evaluating the expression inside the parentheses:

$$\frac{x - 100}{100} = \frac{x}{100} - 1$$

Now, we can substitute this expression back into the original equation:

$$y = 109.95 + 65 \left( \frac{x}{100} - 1 \right)$$

Next, we can distribute the 65 to the terms inside the parentheses:

$$y = 109.95 + 65 \left( \frac{x}{100} \right) - 65$$

Now, we can simplify the equation further by combining like terms:

$$y = 109.95 + \frac{65x}{100} - 65$$

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 5:

$$y = 109.95 + \frac{13x}{20} - 65$$

Finally, we can simplify the constants by combining them:

$$y = 44.95 + \frac{13x}{20}$$

In conclusion, the equation that represents the total cost $y$ (in dollars) of ordering posters from a company that charges a base fee for the first 100 posters and a lower fee for each additional 100 posters is:

$$y = 44.95 + \frac{13x}{20}$$

This equation can be used to calculate the total cost of ordering posters for any number of posters $x$. By plugging in the value of $x$, you can determine the total cost of ordering posters and make informed decisions about your marketing budget.

Let's say you want to order 500 posters. To calculate the total cost, you can plug in $x = 500$ into the equation:

$$y = 44.95 + \frac{13(500)}{20}$$

$$y = 44.95 + 325$$

$$y = 369.95$$

Therefore, the total cost of ordering 500 posters would be $\$369.95$.

When ordering posters, it's essential to consider the cost per poster. To do this, you can divide the total cost by the number of posters:

$$\text{Cost per poster} = \frac{\text{Total cost}}{\text{Number of posters}}$$

For example, if the total cost is $\$369.95$ and the number of posters is 500, the cost per poster would be:

$$\text{Cost per poster} = \frac{369.95}{500}$$

$$\text{Cost per poster} = 0.74$$

Therefore, the cost per poster would be $\$0.74$.

In conclusion, ordering posters can be a cost-effective way to promote your band and attract new fans. By understanding the cost of ordering posters and using the equation to calculate the total cost, you can make informed decisions about your marketing budget and ensure that you get the best value for your money.
You Want to Order Posters to Advertise Your Band: A Cost Analysis and Q&A

As a band, promoting your music and upcoming events is crucial to attracting new fans and increasing your popularity. One effective way to do this is by ordering posters to display in local music stores, coffee shops, and other public areas. However, the cost of ordering posters can add up quickly, especially if you need a large quantity. In this article, we will explore the cost of ordering posters from a company that charges a base fee for the first 100 posters and a lower fee for each additional 100 posters.

Let's assume that the company charges $\$109.95$ for the first 100 posters and $\$65$ for each additional 100 posters. If you order $x$ posters, the total cost $y$ (in dollars) can be represented by the following equation:

$$y = 109.95 + 65 \left( \frac{x - 100}{100} \right)$$

To simplify the equation, we can start by evaluating the expression inside the parentheses:

$$\frac{x - 100}{100} = \frac{x}{100} - 1$$

Now, we can substitute this expression back into the original equation:

$$y = 109.95 + 65 \left( \frac{x}{100} - 1 \right)$$

Next, we can distribute the 65 to the terms inside the parentheses:

$$y = 109.95 + 65 \left( \frac{x}{100} \right) - 65$$

Now, we can simplify the equation further by combining like terms:

$$y = 109.95 + \frac{65x}{100} - 65$$

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 5:

$$y = 109.95 + \frac{13x}{20} - 65$$

Finally, we can simplify the constants by combining them:

$$y = 44.95 + \frac{13x}{20}$$

Q: How much does it cost to order 500 posters? A: To calculate the total cost, you can plug in $x = 500$ into the equation:

$$y = 44.95 + \frac{13(500)}{20}$$

$$y = 44.95 + 325$$

$$y = 369.95$$

Therefore, the total cost of ordering 500 posters would be $\$369.95$.

Q: What is the cost per poster? A: To calculate the cost per poster, you can divide the total cost by the number of posters:

$$\text{Cost per poster} = \frac{\text{Total cost}}{\text{Number of posters}}$$

For example, if the total cost is $\$369.95$ and the number of posters is 500, the cost per poster would be:

$$\text{Cost per poster} = \frac{369.95}{500}$$

$$\text{Cost per poster} = 0.74$$

Therefore, the cost per poster would be $\$0.74$.

Q: How much does it cost to order 1000 posters? A: To calculate the total cost, you can plug in $x = 1000$ into the equation:

$$y = 44.95 + \frac{13(1000)}{20}$$

$$y = 44.95 + 650$$

$$y = 694.95$$

Therefore, the total cost of ordering 1000 posters would be $\$694.95$.

Q: What is the cost per poster for 1000 posters? A: To calculate the cost per poster, you can divide the total cost by the number of posters:

$$\text{Cost per poster} = \frac{\text{Total cost}}{\text{Number of posters}}$$

For example, if the total cost is $\$694.95$ and the number of posters is 1000, the cost per poster would be:

$$\text{Cost per poster} = \frac{694.95}{1000}$$

$$\text{Cost per poster} = 0.69$$

Therefore, the cost per poster would be $\$0.69$.

In conclusion, ordering posters can be a cost-effective way to promote your band and attract new fans. By understanding the cost of ordering posters and using the equation to calculate the total cost, you can make informed decisions about your marketing budget and ensure that you get the best value for your money.