5. To prepare an aquarium for use, you can clean it with a saltwater solution. The amount of salt varies directly with the volume of the water. The solution has 2 teaspoons of aquarium salt for every gallon of water. a. Write an equation that relates 9 gallons of water to ş teaspoons of salt. b. How many teaspoons of aquarium salt are needed for 5 gallons of water?

Let's solve each part step by step. ### a. **Writing the Equation** Since the amount of salt varies **directly** with the volume of water, we can express this relationship with the equation: \[ s = k \times v \] where: - \( s \) = teaspoons of aquarium salt - \( v \) = gallons of water - \( k \) = constant of proportionality Given that there are **2 teaspoons of salt for every gallon of water**, the constant \( k \) is 2. Plugging this into the equation: \[ s = 2v \] **So, the equation relating gallons of water to teaspoons of salt is:** \[ s = 2v \] ### b. **Calculating for 5 Gallons** Using the equation \( s = 2v \): \[ s = 2 \times 5 \] \[ s = 10 \] **Therefore, you need **10 teaspoons** of aquarium salt for 5 gallons of water.** --- **Summary:** - **a.** \( s = 2v \) - **b.** 10 teaspoons of salt are needed for 5 gallons of water.