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Use the information given below to compare the cost of operating a vehicle for three different car owners.

Joe, Tim, and Sue each own a car.

1. **Work Days (Round Trips) Each Month:**
- Joe works 5 days each week.
- Tim works 4 days each week.
- Sue works 3 days each week.
- How many workdays (round trips) does each have per month?

2. **Round Trip Miles per Month:**
- Joe drives 30 miles round trip to work.
- Tim drives 40 miles round trip.
- Sue drives 18 miles round trip.
- Calculate the total round trip miles each driver makes per month.

3. **Gas Cost per Month:**
- Each driver estimates gas consumption at 20 miles per gallon.
- The cost of gas is [tex]$\$1.80$[/tex] per gallon.
- What will be the cost for gas for each driver to go to work?

4. **Insurance Cost per Year:**
- Joe pays [tex]$\$1,920$[/tex] a year for insurance.
- Tim pays [tex]$\$3,000$[/tex] a year for insurance.
- Sue pays [tex]$\$1,080$[/tex] a year for insurance.

5. **Maintenance Cost per Year:**
- Joe pays [tex]$\$1,200$[/tex] a year for maintenance.
- Tim pays [tex]$\$360$[/tex] a year for maintenance because he works on his car himself.
- Sue pays [tex]$\$596$[/tex] a year for maintenance.

6. **Total Cost per Month for Each Driver:**

| | Joe | Tim | Sue |
|-----------------|----------|----------|----------|
| Round trips per month | | | |
| Miles per month | miles | miles | miles |
| Gas cost per month | [tex]$\$$[/tex] | [tex]$\$$[/tex] | [tex]$\$$[/tex] |
| Insurance cost per month | [tex]$\$$[/tex] | [tex]$\$$[/tex] | [tex]$\$$[/tex] |
| Maintenance cost per month | [tex]$\$$[/tex] | [tex]$\$$[/tex] | [tex]$\$$[/tex] |
| Total cost per month | [tex]$\$$[/tex] | [tex]$\$$[/tex] | [tex]$\$$[/tex] |

Calculate the total cost per month for each driver based on the above data.

Answer :

Sure! Let's break down the solution to compare the costs of operating a vehicle for Joe, Tim, and Sue.

### Step 1: Calculate Work Days Each Month

- Joe works 5 days a week. For a 4-week month, he works:
[tex]\[
5 \times 4 = 20 \text{ work days per month}
\][/tex]

- Tim works 4 days a week. For a 4-week month, he works:
[tex]\[
4 \times 4 = 16 \text{ work days per month}
\][/tex]

- Sue works 3 days a week. For a 4-week month, she works:
[tex]\[
3 \times 4 = 12 \text{ work days per month}
\][/tex]

### Step 2: Calculate Round Trip Miles Per Month

- Joe drives 30 miles round trip each day. His monthly miles are:
[tex]\[
30 \times 20 = 600 \text{ miles per month}
\][/tex]

- Tim drives 40 miles round trip each day. His monthly miles are:
[tex]\[
40 \times 16 = 640 \text{ miles per month}
\][/tex]

- Sue drives 18 miles round trip each day. Her monthly miles are:
[tex]\[
18 \times 12 = 216 \text{ miles per month}
\][/tex]

### Step 3: Calculate Gas Cost Per Month

Assuming gas costs [tex]$1.80 per gallon and that each driver gets 20 miles per gallon:

- Joe's gas cost:
\[
\left(\frac{600}{20}\right) \times 1.80 = 54.00 \text{ dollars per month}
\]

- Tim's gas cost:
\[
\left(\frac{640}{20}\right) \times 1.80 = 57.60 \text{ dollars per month}
\]

- Sue's gas cost:
\[
\left(\frac{216}{20}\right) \times 1.80 = 19.44 \text{ dollars per month}
\]

### Step 4: Calculate Insurance and Maintenance Costs Per Month

- Joe pays $[/tex]1,920 annually for insurance and [tex]$1,200 for maintenance:
\[
\text{Insurance: } \frac{1920}{12} = 160 \text{ dollars per month}
\]
\[
\text{Maintenance: } \frac{1200}{12} = 100 \text{ dollars per month}
\]

- Tim pays $[/tex]3,000 annually for insurance and [tex]$360 for maintenance:
\[
\text{Insurance: } \frac{3000}{12} = 250 \text{ dollars per month}
\]
\[
\text{Maintenance: } \frac{360}{12} = 30 \text{ dollars per month}
\]

- Sue pays $[/tex]1,080 annually for insurance and $596 for maintenance:
[tex]\[
\text{Insurance: } \frac{1080}{12} = 90 \text{ dollars per month}
\][/tex]
[tex]\[
\text{Maintenance: } \frac{596}{12} = 49.67 \text{ dollars per month}
\][/tex]

### Step 5: Calculate Total Cost Per Month for Each Driver

- Joe's total cost:
[tex]\[
54.00 + 160 + 100 = 314.00 \text{ dollars per month}
\][/tex]

- Tim's total cost:
[tex]\[
57.60 + 250 + 30 = 337.60 \text{ dollars per month}
\][/tex]

- Sue's total cost:
[tex]\[
19.44 + 90 + 49.67 = 159.11 \text{ dollars per month}
\][/tex]

These calculations give us the total monthly cost for each car owner to operate their vehicles.

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