# A store offers packing and mailing services to customers. The cost of shipping a box is a combination of a flat packing fee of $5 and an amount based on the weight in pounds of the box, $2.25 per pound. Which equation represents the shipping cost as a function of x, the weight in pounds?

**Verified Answer: A store offers packing and mailing services to customers. The cost of shipping a box is a combination of a flat packing fee of $5 and an amount based on the weight in pounds of the box, $2.25 per pound. Which equation represents the shipping cost as a function of x, the weight in pounds?**

**Concept used:**

The concept used in this question is the definition of a function.

A function is a mathematical relationship between the domain and the range values.

In this case, the domain is the weight of the box in pounds (x), and the range is the shipping cost.

The equation in the question represents the shipping cost as a function of the weight in pounds.

This means that for every value of x (the weight of the box in pounds), there is a corresponding value of f(x) (the shipping cost).

In other words, the shipping cost depends on the weight of the box.

For example, if the weight of the box is 5 pounds, the shipping cost can be found by substituting 5 for x in the equation:

f(5) = 5 + 2.25 * 5 f(5) = 5 + 11.25 f(5) = 16.25

Therefore, the shipping cost for a box that weighs 5 pounds is $16.25.

**Step-by-Step Explanation:**

Here is a detailed explanation of how to derive the equation for the shipping cost as a function of the weight in pounds:

- First, we are given that the cost of shipping a box is a combination of a flat packing fee of $5 and an amount based on the weight in pounds of the box.
- The amount based on the weight in pounds is $2.25 per pound.
- To find the total cost of shipping a box, we need to add the flat packing fee to the amount based on the weight in pounds.
- Let’s say the weight of the box is x pounds. The amount based on the weight in pounds is $2.25 per pound, so the total cost for the weight of the box is $2.25 * x pounds.
- To find the total cost of shipping the box, we need to add the flat packing fee of $5 to the cost of the weight of the box, which is $2.25 * x pounds.
- The equation representing the total cost of shipping the box as a function of the weight in pounds (x) is:

Shipping cost = $5 + $2.25 * x (pounds)

This can also be written as:

f(x) = 5 + 2.25x (pounds)

**Alternative Method**

**Solution:** According to the question, it is given that

Cost of packing = $5

Cost per pound = $2.25

Let x be the weight of the box in pounds

**Hence, the required equation that represents the shipping cost as a function of x is f(x) = 2.25x + 5**

**Conclusion**

**A store offers packing and mailing services to customers. The cost of shipping a box is a combination of a flat packing fee of $5 and an amount based on the weight in pounds of the box, $2.25 per pound. The equation that represents the shipping cost as a function of x the weight in pounds is f (x) = 2.25x + 5**