Question 1170145
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.