5. A salt water aquarium requires a very careful balance of water and salt. The ratio of fresh water to salt water is 15 to 1 . If I use 48 more gallons of water to fill my tank than I do salt water, how many gallons of salt water will I use? How many total gallons of water will be in the tank?

Let's say the amount of salt water you use is \( x \) gallons. According to the given ratio of fresh water to salt water, for every gallon of salt water, you need 15 gallons of fresh water. Therefore, the fresh water will be \( 15x \) gallons. You've added that you use 48 more gallons of fresh water than salt water, which gives us the equation: \[ 15x = x + 48 \] Now, let's solve the equation: \[ 15x - x = 48 \] \[ 14x = 48 \] \[ x = \frac{48}{14} = \frac{24}{7} \approx 3.43 \text{ gallons of salt water} \] Next, we can find out how much fresh water is used: \[ 15x = 15 \times \frac{24}{7} = \frac{360}{7} \approx 51.43 \text{ gallons of fresh water} \] To find the total gallons of water in the tank: \[ \text{Total water} = \text{Fresh water} + \text{Salt water} = \frac{360}{7} + \frac{24}{7} = \frac{384}{7} \approx 54.86 \text{ gallons} \] So, the amount of salt water used is approximately 3.43 gallons, and the total amount of water in the tank is approximately 54.86 gallons.