Question

The aquarium is draining a

large fish tank. The pump they are
using can drain 24 gallons per hour.
After 3 hours, there are 78 gallons
left in the tank.
a) Write an equation to model the
water left in the tank after, y,
after x hours of draining.
b) How many gallons were
originally in the tank?

Answer 1

The equation modeling the water left in the tank after x hours is y = -24x + 150, where x is the number of hours the tank has been draining. The original amount of water in the tank was 150 gallons.

Step-by-step explanation:

To model the water left in the tank after x hours of draining, we can use a linear equation. Since the pump drains 24 gallons per hour, and after 3 hours there are 78 gallons left, we can set up our equation as:

y = mx + b

Where y is the amount of water left in the tank, m is the rate of draining (-24 gallons/hour), x is the number of hours, and b is the initial amount of water in the tank.

After 3 hours of draining (x=3), there are 78 gallons left (y=78). Plugging these values into the equation gives us:

78 = -24(3) + b, which simplifies to 78 = -72 + b. Therefore, b = 78 + 72 = 150 gallons.

So, the equation is y = -24x + 150, and the original amount of water in the tank was 150 gallons.