SOLUTION: 4. Jolene is starting a dog walking company. She is considering two different plans to charge her
clients.
a. In plan one, she charges a monthly fee of $20, and then $5 for each
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Question 1170145: 4. Jolene is starting a dog walking company. She is considering two different plans to charge her
clients.
a. In plan one, she charges a monthly fee of $20, and then $5 for each time she walks a
dog. Write an equation to represent this plan for charging.
b. Identify the Independent Variable, Dependent Variable, y-intercept and
coefficient/unit rate in the equation you wrote.
c. For plan two, she writes the following equation. πΌπΌ = 7.5ππ I = Income d=number of
dogs walked. Identify the Independent Variable, Dependent Variable, y-intercept and
coefficient/unit rate.
d. How many dogs does she need to walk to make the same amount of money from
both plans?
e. Which plan do you think she should use and why?
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Absolutely, let's break down Jolene's dog walking company plans.
**a. Plan One Equation:**
Let:
* 'I' represent the income Jolene earns.
* 'd' represent the number of times she walks a dog.
The equation for Plan One is:
* I = 5d + 20
**b. Plan One Variables and Values:**
* **Independent Variable:** d (number of times she walks a dog)
* **Dependent Variable:** I (income)
* **y-intercept:** 20 (This represents the monthly fee, even if she walks no dogs.)
* **Coefficient/Unit Rate:** 5 (This represents the amount she earns per dog walk.)
**c. Plan Two Variables and Values:**
* **Equation:** I = 7.5d
* **Independent Variable:** d (number of times she walks a dog)
* **Dependent Variable:** I (income)
* **y-intercept:** 0 (There is no monthly fee. If she walks no dogs, she earns nothing.)
* **Coefficient/Unit Rate:** 7.5 (This represents the amount she earns per dog walk.)
**d. Number of Dog Walks for Equal Income:**
To find out when the income from both plans is the same, we set the two equations equal to each other:
* 5d + 20 = 7.5d
Now, solve for 'd':
1. Subtract 5d from both sides: 20 = 2.5d
2. Divide both sides by 2.5: d = 8
Therefore, Jolene needs to walk 8 dogs to make the same amount of money from both plans.
**e. Which Plan to Use and Why:**
* **If Jolene plans to walk fewer than 8 dogs per month:** Plan One would be better. Even if she walks zero dogs she earns $20.
* **If Jolene plans to walk more than 8 dogs per month:** Plan Two would be better. She earns $7.50 per dog walk, versus $5 per dog walk in plan one.
* **Considerations:**
* **Customer Base:** If Jolene has a consistent client base that guarantees many dog walks, Plan Two is more profitable.
* **Upfront Costs:** If Jolene has initial costs (e.g., advertising, supplies), Plan One's monthly fee could help cover those.
* **Time Commitment:** Plan Two rewards more time spent walking dogs, while Plan One provides a base income regardless of the number of walks.
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