A Hotel Buyer Is Ordering New Towels For All Of The Rooms In The Hotel. Hand Towels Cost $\$1$ Each And Bath Towels Cost $\$4$. The Total Expenditure Must Be Under $\$3,300$.Write The Inequality In Standard Form That

Introduction

When it comes to managing a hotel's expenses, every detail matters. In this scenario, a hotel buyer is tasked with ordering new towels for all the rooms in the hotel. The buyer must ensure that the total expenditure does not exceed $\$3,300$. To make this decision, the buyer needs to consider the cost of hand towels and bath towels. In this article, we will explore how to write an inequality in standard form that represents the total expenditure on towels.

Understanding the Costs

The hotel buyer has two types of towels to purchase: hand towels and bath towels. Hand towels cost $\$1$ each, while bath towels cost $\$4$ each. To represent the total expenditure on towels, we need to consider the number of hand towels and bath towels purchased.

Writing the Inequality

Let's denote the number of hand towels purchased as $h$ and the number of bath towels purchased as $b$. The total expenditure on hand towels is $\$1 \times h = \$h$, and the total expenditure on bath towels is $\$4 \times b = \$4b$. The total expenditure on all towels is the sum of the expenditures on hand towels and bath towels, which is $\$h + \$4b$.

Since the total expenditure must be under $\$3,300$, we can write the inequality:

$$h + 4b < 3300$$

Standard Form of the Inequality

To write the inequality in standard form, we need to isolate the variable on one side of the inequality sign. In this case, we can subtract $h$ from both sides of the inequality to get:

$$4b < 3300 - h$$

However, we can rewrite the inequality in a more standard form by dividing both sides by $4$:

$$b < \frac{3300 - h}{4}$$

Conclusion

In this article, we have written an inequality in standard form that represents the total expenditure on towels. The inequality is:

$$b < \frac{3300 - h}{4}$$

This inequality can be used by the hotel buyer to determine the maximum number of bath towels that can be purchased, given the number of hand towels purchased.

Example

Suppose the hotel buyer wants to purchase $200$ hand towels. To find the maximum number of bath towels that can be purchased, we can substitute $h = 200$ into the inequality:

$$b < \frac{3300 - 200}{4}$$

Simplifying the expression, we get:

$$b < \frac{3100}{4}$$

$$b < 775$$

Therefore, the hotel buyer can purchase at most $775$ bath towels, given that $200$ hand towels are purchased.

Applications

This inequality can be applied in various scenarios, such as:

• A hotel buyer wants to purchase towels for a new hotel wing, and the total expenditure must be under $\$10,000$.
• A retailer wants to purchase towels for a store, and the total expenditure must be under $\$5,000$.

In both cases, the inequality can be used to determine the maximum number of bath towels that can be purchased, given the number of hand towels purchased.

Final Thoughts

In conclusion, writing an inequality in standard form is a crucial step in solving problems involving inequalities. By following the steps outlined in this article, we can write an inequality that represents the total expenditure on towels. This inequality can be used by hotel buyers, retailers, and other individuals to make informed decisions about towel purchases.

Introduction

In our previous article, we explored how to write an inequality in standard form that represents the total expenditure on towels. A hotel buyer is tasked with ordering new towels for all the rooms in the hotel, and the total expenditure must be under $\$3,300$. In this Q&A article, we will answer some common questions related to writing inequalities for towel purchases.

Q: What is the purpose of writing an inequality for towel purchases?

A: The purpose of writing an inequality for towel purchases is to determine the maximum number of bath towels that can be purchased, given the number of hand towels purchased. This helps the hotel buyer make informed decisions about towel purchases and ensures that the total expenditure does not exceed the budget.

Q: How do I write an inequality for towel purchases?

A: To write an inequality for towel purchases, you need to consider the cost of hand towels and bath towels. Let's denote the number of hand towels purchased as $h$ and the number of bath towels purchased as $b$. The total expenditure on hand towels is $\$1 \times h = \$h$, and the total expenditure on bath towels is $\$4 \times b = \$4b$. The total expenditure on all towels is the sum of the expenditures on hand towels and bath towels, which is $\$h + \$4b$. Since the total expenditure must be under $\$3,300$, we can write the inequality:

$$h + 4b < 3300$$

Q: What if I want to purchase a specific number of hand towels? How do I adjust the inequality?

A: If you want to purchase a specific number of hand towels, you can substitute that number into the inequality. For example, if you want to purchase $200$ hand towels, you can substitute $h = 200$ into the inequality:

$$200 + 4b < 3300$$

Simplifying the expression, we get:

$$4b < 3100$$

$$b < 775$$

Therefore, you can purchase at most $775$ bath towels, given that $200$ hand towels are purchased.

Q: Can I use this inequality for other types of purchases?

A: Yes, you can use this inequality for other types of purchases. For example, if you want to purchase towels for a store, and the total expenditure must be under $\$5,000$, you can write the inequality:

$$h + 4b < 5000$$

Q: What if I want to purchase towels with different costs? How do I adjust the inequality?

A: If you want to purchase towels with different costs, you can adjust the inequality accordingly. For example, if hand towels cost $\$2$ each and bath towels cost $\$5$ each, you can write the inequality:

$$2h + 5b < 3300$$

Q: Can I use this inequality for multiple purchases?

A: Yes, you can use this inequality for multiple purchases. For example, if you want to purchase towels for multiple hotel rooms, and the total expenditure must be under $\$10,000$, you can write the inequality:

$$h + 4b < 10000$$

Q: What if I want to purchase towels with a discount? How do I adjust the inequality?

A: If you want to purchase towels with a discount, you can adjust the inequality accordingly. For example, if you get a $10\%$ discount on all towel purchases, you can write the inequality:

$$h + 4b < 0.9 \times 3300$$

Simplifying the expression, we get:

$$h + 4b < 2970$$

Conclusion

In this Q&A article, we have answered some common questions related to writing inequalities for towel purchases. By following the steps outlined in this article, you can write an inequality that represents the total expenditure on towels. This inequality can be used by hotel buyers, retailers, and other individuals to make informed decisions about towel purchases.