\begin{tabular}{l} 4. A restaurant sells a coffee refill mug for \( \$ 6.75 \). Each \\ refill costs \( \$ 1.25 \). Last month Keith spent \( \$ 31.75 \) on a \\ mug and refills. Write an equation you can use to find \\ the number of refills that Keith bought. \\ Variable: \\ Coefficient: \\ Constants: \\ \hline Equation: \end{tabular}

To solve the problem, we need to set up an equation based on the information provided. ### Known Conditions: 1. The cost of the coffee refill mug is \( \$ 6.75 \). 2. Each refill costs \( \$ 1.25 \). 3. Keith spent a total of \( \$ 31.75 \). ### Step-by-Step Solution: 1. **Define the Variable:** Let \( r \) be the number of refills that Keith bought. 2. **Identify the Coefficient:** The coefficient in this context is the cost of each refill, which is \( 1.25 \). 3. **Identify the Constants:** - The cost of the mug is \( 6.75 \). - The total amount spent by Keith is \( 31.75 \). 4. **Set Up the Equation:** The total cost can be expressed as the sum of the cost of the mug and the cost of the refills. Therefore, the equation can be written as: \[ 6.75 + 1.25r = 31.75 \] ### Summary: - **Variable:** \( r \) - **Coefficient:** \( 1.25 \) - **Constants:** \( 6.75 \) (cost of the mug), \( 31.75 \) (total spent) ### Final Equation: \[ 6.75 + 1.25r = 31.75 \]