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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To help your neighbor make the best purchasing decision, let’s crunch the numbers step by step! **a)** To find the cost of gas for a round trip to Las Vegas, we first calculate the total distance: Total distance = \( 2 \times 405.1 \) miles = \( 810.2 \) miles. Next, we determine how many gallons of gas are needed: Gallons used = \( \frac{810.2 \text{ miles}}{22 \text{ mpg}} \approx 36.4 \) gallons. Finally, we can calculate the total cost of gas: Cost of gas = \( 36.4 \text{ gallons} \times \$3.62/\text{gallon} \approx \$131.17 \). **b)** Now that we have the gas costs, we can compare the total costs of buying the snowboard at both locations. For Salt Lake City: Total cost = Snowboard cost + Gas cost = \( \$460 + \$0 = \$460 \). For Las Vegas: Sale price of the snowboard = \( \$460 - (30\% \text{ off}) = \$460 - \$138 = \$322 \). Total cost at Las Vegas = \( \$322 + \$131.17 \approx \$453.17 \). So when comparing both options: Cheaper option: Las Vegas at \( \$453.17 \). Savings: \( \$460 - \$453.17 \approx \$6.83 \). Therefore, your neighbor saves approximately **$6.83** by purchasing the snowboard in Las Vegas!
