2. Val rented a bicycle while she was on vacation. She paid a flat rental fee of $$ \$ 55.00 $$, plus $$ \$ 8.50 $$ each day. The total cost was $$ \$ 123 $$. Write an equation you can use to find the number of days she rented the bicycle. Variable: Coefficient: Constants:

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To solve this problem, we'll create an equation that represents the total cost Val paid for renting the bicycle.

### **Equation:**
$$ 55 + 8.50d = 123 $$

### **Components:**

- **Variable:** $$ d $$  
  Represents the number of days Val rented the bicycle.

- **Coefficient:** $$ 8.50 $$  
  This is the cost per day for renting the bicycle.

- **Constants:** $$ 55 $$ and $$ 123 $$  
  - **55:** The flat rental fee that Val paid regardless of the number of days.
  - **123:** The total cost Val ended up paying.

### **Explanation:**

- **Flat Rental Fee:** Val pays a one-time fee of \$55.00 when she rents the bicycle. This is a constant because it doesn't change with the number of days rented.

- **Daily Cost:** For each day Val rents the bicycle, she pays an additional \$8.50. Here, 8.50 is the coefficient of the variable $$ d $$, which stands for the number of days.

- **Total Cost:** The sum of the flat fee and the daily costs equals the total amount Val paid, which is \$123.00.

By setting up the equation $$ 55 + 8.50d = 123 $$, you can solve for $$ d $$ to find out how many days Val rented the bicycle.

### **Solving for $$ d $$:**

$$ 
\begin{align*}
55 + 8.50d &= 123 \
8.50d &= 123 - 55 \
8.50d &= 68 \
d &= \frac{68}{8.50} \
d &= 8 \text{ days}
\end{align*}
$$

Val rented the bicycle for **8 days**.
**Equation:** $$ 55 + 8.50d = 123 $$ **Components:** - **Variable:** $$ d $$ (number of days) - **Coefficient:** \$8.50 (cost per day) - **Constants:** \$55 (flat fee), \$123 (total cost)

2. Val rented a bicycle while she was on vacation. She paid a flat rental fee of \( \$ 55.00 \), plus \( \$ 8.50 \) each day. The total cost was \( \$ 123 \). Write an equation you can use to find the number of days she rented the bicycle. Variable: Coefficient: Constants:

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