Your neighbor is looking at getting a new snowboard for this winter and has been shopping around. They found the perfect board and noticed it is being sold at two different locations, one here in Salt Lake City and one in Las Vegas. The store here in Salt Lake City is selling the snowboard for $$ \$ 460 $$, while the store in Las Vegas has a $$ 30 \% $$ off sale. They are not sure if it is worth driving to Las Vegas to get the board at the cheaper price because they know the gas will cost money too, so they ask you for help. First, determine what information you need to answer this question, then click here to display that info (along with other info). - How far is the drive? Google.maps gives the driving distance in one direction as 405.1 miles. - How long does the drive take? Google.maps gives the driving time in one direction as 6 hours and 15 minutes. What kind of mileage does your car get? It averages about 22 miles per gallon on the highway. How many gallons does your car hold? About 17 gallons How much is gas? About $$ \$ 3.62 / $$ gallon right now. a) How much would it cost in gas to drive to Las Vegas and back? $$ \$ $$ b) Which of the two options ends up being cheaper when we consider the cost of gas and the cost of the snowboard? Buying the snowboard in Salt Lake City Buying the snowboard in Las Vegas o $$ \$ $$ How much does the cheaper option save you? Write final answer to the nearest cent.

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UpStudy AI · Accepted Answer

**1. Calculate the roundtrip distance.**  
The one-way distance is given as  
$$
405.1 \text{ miles}.
$$  
Thus, the roundtrip distance is  
$$
2 \times 405.1 = 810.2 \text{ miles}.
$$

**2. Compute the total gallons of gas used.**  
The car averages $$22$$ miles per gallon, so the number of gallons used is  
$$
\frac{810.2}{22} \approx 36.83 \text{ gallons}.
$$

**3. Determine the cost of the gas for the roundtrip.**  
With gas costing $$\$3.62$$ per gallon, the gas cost is  
$$
36.83 \times 3.62 \approx 133.32 \text{ dollars}.
$$

**4. Compute the cost to buy the snowboard in each location.**

- **Salt Lake City:**  
  The price is given as  
  $$
  \$460.
  $$

- **Las Vegas:**  
  A $$30\%$$ discount off the $$\$460$$ price gives a discount amount of  
  $$
  0.30 \times 460 = 138 \text{ dollars}.
  $$  
  Thus, the sale price is  
  $$
  460 - 138 = 322 \text{ dollars}.
  $$

**5. Calculate the total cost for buying the snowboard in Las Vegas including gas.**  
Adding the gas cost to the discounted price yields  
$$
322 + 133.32 = 455.32 \text{ dollars}.
$$

**6. Compare the two options.**

- **Salt Lake City cost:** $$\$460$$.  
- **Las Vegas cost:** $$\$455.32$$.

The Las Vegas option is cheaper. The savings are  
$$
460 - 455.32 = 4.68 \text{ dollars}.
$$

**Final Answers:**  
a) The cost in gas for the roundtrip drive is $$\$133.32$$.  
b) Buying the snowboard in Las Vegas is cheaper, saving $$\$4.68$$ over buying it in Salt Lake City.
**Gas Cost:** \$133.32 **Cheaper Option:** Buying in Las Vegas **Savings:** \$4.68

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