7. Ethan uses a \( \$ 30 \) gift card to buy his favorite drink at a coffee shop. The drink costs \( \$ 3 \), including sales tax. He buys the same drink a number of times, and he does not buy anything else with the card. If the card has \( \$ 12 \) left, how many times does Ethan buy the drink? Write and solve an equation. Check your solution.

To determine how many times Ethan buys his favorite drink using the gift card, let's break down the problem step by step. ### **Step 1: Define the Variable** Let: - \( x \) = the number of times Ethan buys the drink. ### **Step 2: Set Up the Equation** Each drink costs \( \$3 \), so the total amount Ethan spends on \( x \) drinks is: \[ 3x \] Ethan starts with a \( \$30 \) gift card and has \( \$12 \) left after his purchases. Therefore, the amount he spent is: \[ 30 - 12 = 18 \] So, we can set up the equation: \[ 3x = 18 \] ### **Step 3: Solve the Equation** Divide both sides of the equation by 3 to find \( x \): \[ \begin{align*} 3x &= 18 \\ x &= \frac{18}{3} \\ x &= 6 \end{align*} \] ### **Step 4: Check the Solution** To ensure our solution is correct, let's verify it: - If Ethan buys the drink 6 times, he spends: \[ 6 \times \$3 = \$18 \] - Subtracting this from the initial gift card amount: \[ \$30 - \$18 = \$12 \] Since the remaining amount matches the given information, our solution is correct. ### **Answer** Ethan buys the drink **6 times**.