Question
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?
Ask by Wilson Wade. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
a. The equation is \( s = 2v \).
b. You need 10 teaspoons of aquarium salt for 5 gallons of water.
Solution
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.**
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**Summary:**
- **a.** \( s = 2v \)
- **b.** 10 teaspoons of salt are needed for 5 gallons of water.
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Simplify this solution Beyond the Answer
To relate 9 gallons of water to salt, you can use the equation \( s = 2g \), where \( s \) is the number of teaspoons of salt and \( g \) is the gallons of water. For 9 gallons, the equation becomes \( s = 2(9) = 18 \) teaspoons of salt. For 5 gallons of water, simply apply the same relationship. Using the equation \( s = 2g \), plug in 5 for \( g \): \( s = 2(5) = 10 \) teaspoons of aquarium salt are needed. Keep your aquatic friends healthy and happy with the right measurements!
