Based on your Part 2 answers, how much will it cost to deliver the topsoil? 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. 110400 $$ =63.89 $$ $$ =237 $$ 48 What is the total cost (in gas) to deliver the soil in the pickup truck? How many trips will you need to make in your truck? 103.36 Comparing cost for Final Decision Which option is cheaper? use own truck How much cheaper is it? $$ \$ 12764 $$

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To solve the problem, we need to follow these steps:

1. **Calculate the volume of the truck bed.**
2. **Determine how much topsoil can be delivered in one trip.**
3. **Calculate the total cost of gas for one trip.**
4. **Determine how many trips are needed to deliver the total amount of topsoil.**
5. **Compare the costs of using the truck versus the delivery service.**

### Step 1: Calculate the Volume of the Truck Bed

The volume $$ V $$ of a rectangular prism (the truck bed) can be calculated using the formula:

$$
V = l \times w \times h
$$

Where:
- $$ l = 80 $$ inches
- $$ w = 69 $$ inches
- $$ h = 20 $$ inches

First, we need to convert the dimensions from inches to feet (since there are 12 inches in a foot):

$$
l = \frac{80}{12} \text{ ft}, \quad w = \frac{69}{12} \text{ ft}, \quad h = \frac{20}{12} \text{ ft}
$$

Now, let's calculate the volume in cubic feet.

### Step 2: Calculate the Volume

Calculating the volume:

$$
V = \left(\frac{80}{12}\right) \times \left(\frac{69}{12}\right) \times \left(\frac{20}{12}\right)
$$

### Step 3: Calculate the Total Cost of Gas for One Trip

To calculate the total cost of gas for one trip, we need to find the distance traveled and the gas consumption.

1. **Distance to the store and back:**
   $$
   \text{Total Distance} = 2 \times 6 \text{ miles} = 12 \text{ miles}
   $$

2. **Gas consumption:**
   $$
   \text{Gas Used} = \frac{\text{Total Distance}}{\text{Miles per Gallon}} = \frac{12}{17} \text{ gallons}
   $$

3. **Cost of gas:**
   $$
   \text{Cost of Gas} = \text{Gas Used} \times \text{Cost per Gallon} = \left(\frac{12}{17}\right) \times 3.04
   $$

### Step 4: Determine How Many Trips are Needed

Assuming you have a total volume of topsoil to deliver (let's denote it as $$ T $$), the number of trips $$ N $$ needed can be calculated as:

$$
N = \frac{T}{V}
$$

### Step 5: Compare Costs

Finally, we can compare the total cost of using the truck (including gas for all trips) with the cost of the delivery service.

Now, let's perform the calculations.

First, I will calculate the volume of the truck bed.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{80}{12}\right)\left(\frac{69}{12}\right)\left(\frac{20}{12}\right)$$
- step1: Reduce the fraction:
  $$\frac{20}{3}\left(\frac{69}{12}\right)\left(\frac{20}{12}\right)$$
- step2: Reduce the fraction:
  $$\frac{20}{3}\times \frac{23}{4}\left(\frac{20}{12}\right)$$
- step3: Reduce the fraction:
  $$\frac{20}{3}\times \frac{23}{4}\times \frac{5}{3}$$
- step4: Multiply the terms:
  $$\frac{115}{3}\times \frac{5}{3}$$
- step5: Multiply the fractions:
  $$\frac{115\times 5}{3\times 3}$$
- step6: Multiply:
  $$\frac{575}{9}$$
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 $$ T/(575/9) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{T}{\frac{575}{9}}$$
- step1: Multiply by the reciprocal:
  $$T\times \frac{9}{575}$$
- step2: Multiply the terms:
  $$\frac{T\times 9}{575}$$
- step3: Multiply the terms:
  $$\frac{9T}{575}$$
### Step 1: Calculate the Volume of the Truck Bed

The volume of the truck bed is:

$$
V = \frac{575}{9} \text{ cubic feet} \approx 63.89 \text{ cubic feet}
$$

### Step 2: Calculate the Total Cost of Gas for One Trip

The cost of gas for one trip is approximately:

$$
\text{Cost of Gas} \approx 2.15
$$

### Step 3: Determine How Many Trips are Needed

If we denote the total volume of topsoil to deliver as $$ T $$ (in cubic feet), the number of trips $$ N $$ needed is:

$$
N = \frac{9T}{575}
$$

### Step 4: Total Cost of Gas for All Trips

The total cost of gas for all trips can be calculated as:

$$
\text{Total Cost} = N \times \text{Cost of Gas} = \left(\frac{9T}{575}\right) \times 2.15
$$

### Step 5: Compare Costs

To compare the costs, we need the total cost of the delivery service and the total cost of using the truck.

If the delivery service cost is $$ C_d $$ and the total cost of using the truck is $$ C_t $$, we can find out how much cheaper using the truck is:

$$
\text{Difference} = C_d - C_t
$$

Given that the delivery service cost is $$ \$ 12764 $$, we can now calculate the total cost of using the truck and find the difference.

Let's assume $$ T $$ is the total volume of topsoil you want to deliver. If you provide that value, I can calculate the exact costs. Otherwise, I can summarize the calculations based on the formulas derived.
To determine the cost of delivering topsoil using your pickup truck, follow these steps: 1. **Calculate the truck bed volume:** - Length: 80 inches = 6.6667 feet - Width: 69 inches = 5.75 feet - Height: 20 inches = 1.6667 feet - Volume = 6.6667 * 5.75 * 1.6667 ≈ 63.89 cubic feet 2. **Determine the number of trips needed:** - Total topsoil volume (T) in cubic feet - Number of trips = T / 63.89 3. **Calculate the cost of gas per trip:** - Distance: 6 miles each way = 12 miles total - Miles per gallon: 17 - Gallons used = 12 / 17 ≈ 0.7059 gallons - Cost per trip = 0.7059 * \$3.04 ≈ \$2.15 4. **Total gas cost for all trips:** - Total cost = Number of trips * \$2.15 5. **Compare costs:** - Delivery service cost: \$12,764 - Truck delivery cost: Total gas cost - Difference = \$12,764 - Total gas cost **Conclusion:** Using your pickup truck is cheaper than the delivery service. The exact savings depend on the total volume of topsoil you need to deliver.

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