Based on your Part 2 answers, how much will it cost to deliver the topsoil? \$ 175 Cost for Pickup You want to compare this to picking up the soil yourself. The truck you have available has a bed that is 80 inches long, 69 inches wide, and 20 inches tall. The store is 6 miles away and it takes about 20 minutes to drive there. The truck averages about 17 miles per gallon and gas costs \( \$ 3.04 \) per gallon. What is the volume of topsoil that you can fit in the truck without it spilling over? Round answers to two decimal places, if needed. \( \square \) \[ 110400 \] cubic inches \[ \begin{array}{l} =63.89 \quad \text { cubic feet } \\ =2.37 \quad \sim \text { cubic yards } \end{array} \] How many trips will you need to make in your truck? \( \square \) 36 trips in the truck What is the total cost (in gas) to deliver the soil in the pickup truck? \( \$ \) \( \square \) Enscran integar or debimal number, with 2 trailmal pisces [more]] Comparing Cost for Final Decision Which option is cheaper? use own truck \( \checkmark \checkmark \) How much cheaper is it? \$ \( \square \) 166.64

Let's break down the problem step by step to find the total cost of delivering the topsoil using your truck. ### Step 1: Calculate the Volume of the Truck Bed The volume \( V \) of the truck bed can be calculated using the formula for the volume of a rectangular prism: \[ V = \text{length} \times \text{width} \times \text{height} \] Given: - Length = 80 inches - Width = 69 inches - Height = 20 inches Calculating the volume in cubic inches: \[ V = 80 \times 69 \times 20 \] ### Step 2: Convert Volume to Cubic Feet and Cubic Yards To convert cubic inches to cubic feet, use the conversion factor \( 1 \text{ cubic foot} = 1728 \text{ cubic inches} \): \[ \text{Cubic feet} = \frac{V}{1728} \] To convert cubic feet to cubic yards, use the conversion factor \( 1 \text{ cubic yard} = 27 \text{ cubic feet} \): \[ \text{Cubic yards} = \frac{\text{Cubic feet}}{27} \] ### Step 3: Calculate the Number of Trips Given that the total volume of topsoil needed is \( 110400 \) cubic inches, we can find the number of trips required by dividing the total volume by the volume of the truck bed: \[ \text{Number of trips} = \frac{\text{Total volume}}{\text{Volume of truck bed}} \] ### Step 4: Calculate the Total Cost of Gas 1. **Distance to the store**: 6 miles (one way), so round trip is \( 12 \) miles. 2. **Fuel efficiency**: 17 miles per gallon. 3. **Gas cost**: \( \$3.04 \) per gallon. First, calculate the gallons of gas needed for one round trip: \[ \text{Gallons needed} = \frac{\text{Total distance}}{\text{Miles per gallon}} = \frac{12}{17} \] Then, calculate the cost of gas for one round trip: \[ \text{Cost of gas for one trip} = \text{Gallons needed} \times \text{Gas cost} \] Finally, multiply the cost of gas for one trip by the number of trips to get the total cost of gas. ### Step 5: Compare Costs Now, we can compare the total cost of using the truck with the cost of delivery \( \$175 \) and find out how much cheaper it is to use the truck. Let's perform the calculations. Calculate the value by following steps: - step0: Calculate: \(\frac{110400}{\left(80\times 69\times 20\right)}\) - step1: Remove the parentheses: \(\frac{110400}{80\times 69\times 20}\) - step2: Multiply the terms: \(\frac{110400}{110400}\) - step3: Reduce the fraction: \(1\) Calculate or simplify the expression \( (12/17)*3.04 \). Calculate the value by following steps: - step0: Calculate: \(\frac{12}{17}\times 3.04\) - step1: Convert the expressions: \(\frac{12}{17}\times \frac{76}{25}\) - step2: Multiply the fractions: \(\frac{12\times 76}{17\times 25}\) - step3: Multiply the terms: \(\frac{912}{17\times 25}\) - step4: Multiply the terms: \(\frac{912}{425}\) Calculate or simplify the expression \( 80*69*20 \). Calculate the value by following steps: - step0: Calculate: \(80\times 69\times 20\) - step1: Multiply the terms: \(5520\times 20\) - step2: Multiply the numbers: \(110400\) Calculate or simplify the expression \( 12/17 \). Calculate the value by following steps: - step0: Calculate: \(\frac{12}{17}\) Calculate or simplify the expression \( (12/17)*3.04*1 \). Calculate the value by following steps: - step0: Calculate: \(\frac{12}{17}\times 3.04\times 1\) - step1: Rewrite the expression: \(\frac{12}{17}\times 3.04\) - step2: Convert the expressions: \(\frac{12}{17}\times \frac{76}{25}\) - step3: Multiply the fractions: \(\frac{12\times 76}{17\times 25}\) - step4: Multiply the terms: \(\frac{912}{17\times 25}\) - step5: Multiply the terms: \(\frac{912}{425}\) Calculate or simplify the expression \( 175 - 2.145882 \). Calculate the value by following steps: - step0: Calculate: \(175-2.145882\) - step1: Subtract the numbers: \(172.854118\) ### Summary of Calculations 1. **Volume of the Truck Bed**: - The volume of the truck bed is \( 110400 \) cubic inches. 2. **Number of Trips**: - You will need to make \( 1 \) trip to deliver the topsoil. 3. **Total Cost of Gas for One Trip**: - The total cost of gas for one round trip is approximately \( \$2.15 \). 4. **Comparison of Costs**: - The cost of delivery using the truck is \( \$2.15 \). - The cost of delivery from the store is \( \$175 \). - The savings by using your own truck is approximately \( \$172.85 \). ### Final Answers - **Total Cost (in gas) to deliver the soil in the pickup truck**: \( \$2.15 \) - **How much cheaper is it?**: \( \$172.85 \) Thus, using your own truck is significantly cheaper than the delivery option.