Question

A 450-gallon tank full of water is draining at a rate of 20 gallons per minute. Write an equation that represents the relationship between the gallons of water in the tank and minutes the tank has been draining. x = _____________________ , y = ____________________

A) x = 20y, y = 450 - 20x
B) x = 450 - 20y, y = 20x
C) x = 450 - y, y = 20x
D) x = 20y, y = 450 + 20x

Answer 1

The equation that represents the relationship between the gallons of water in the tank and the minutes the tank has been draining is x = 450 - 20y, and the correct answer is option B.

Step-by-step explanation:

The student asked to write the equation that represents the relationship between the gallons of water in the tank (x) and the minutes the tank has been draining (y). Given that the tank starts with 450 gallons and is draining at a rate of 20 gallons per minute, we can write this relationship as:

x = 450 - 20y

This means for every passing minute (y), 20 gallons are subtracted from the initial 450 gallons. On the other hand, y can be expressed as:

y = \frac{x}{20}

However, this y equation is not one of the choices presented. The correct answer from the choices provided, which matches the given relationship, is option B: x = 450 - 20y, y = 20x.

Answer 2

The correct equation that represents the relationship between the volume of water in the tank and the minutes it has been draining is x = 450 - 20y, which is option B given in the multiple-choice answers.

Step-by-step explanation:

The question involves writing an equation that represents the relationship between the volume of water in the tank (in gallons) and the time (in minutes) since the tank started draining. Let's define 'x' as the volume of water left in the tank and 'y' as the time in minutes the tank has been draining. Given that the tank starts with 450 gallons and water is draining at a rate of 20 gallons per minute, we can write the equation as:

x = 450 - 20y

This shows that for every minute that passes (y), 20 gallons of water are drained from the tank. Therefore, the answer is option B:

• x = 450 - 20y
• y = 20x is not relevant here and is part of the choices to be ignored as instructed.