Question

Question was provided via image upload.

Explanation:

Identify visible data

The image shows travel cost data for two destinations:

• Destination 1 (Las Vegas, Nevada):
• Round trip flight: \(F_1 = \$65\)
• Hotel cost per night: \(H_1 = \$68\)
• Destination 2 (Los Angeles, California):
• Round trip flight: \(F_2 = \$67\)
• Hotel cost per night: \(H_2 = \$71\)

Formulate cost equations

Let \(x\) represent the number of nights stayed.
The total cost \(C_1(x)\) for Destination 1 is:

$$C_1(x) = 68x + 65$$

The total cost \(C_2(x)\) for Destination 2 is:

$$C_2(x) = 71x + 67$$

Analyze cost comparison

We compare the total costs for any number of nights \(x \ge 1\):

• For \(x = 1\):

$$C_1(1) = 68(1) + 65 = 133$$

$$C_2(1) = 71(1) + 67 = 138$$

• Since both the initial flight cost and the nightly hotel rate are cheaper for Destination 1 than for Destination 2:

$$65 < 67 \quad \text{and} \quad 68 < 71$$

Destination 1 (Las Vegas) will always be cheaper than Destination 2 (Los Angeles) for any number of nights stayed.

Answer:

Based on the visible table data, we can construct the total cost equations for staying \(x\) nights at each destination:

• Destination 1 (Las Vegas, Nevada):

$$\text{Total Cost} = 68x + 65$$

• Destination 2 (Los Angeles, California):

$$\text{Total Cost} = 71x + 67$$

Since both the flight cost (\(\$65 < \$67\)) and the nightly hotel rate (\(\$68 < \$71\)) are lower for Destination 1, Destination 1 (Las Vegas) is always the more economical choice for any number of nights.