Math Problem Statement

A pool is being filled at a constant rate. After x hours, the pool has y gallons of water. The amount of water in the pool can be modeled by the equation y = 60x + 250. What does the 60 represent in this equation?

Solution

The equation provided in the question is y=60x+250y = 60x + 250, where:

  • yy represents the amount of water in the pool after xx hours.
  • 60x60x suggests that the water is being filled at a constant rate.

In this context, the number 60 represents the rate at which the pool is being filled, measured in gallons per hour. Hence, the correct answer is:

  • the rate at which the pool is being filled

Would you like more details on how to interpret linear equations in this context?

Here are five related questions to consider:

  1. What does the 250 represent in this equation?
  2. How would the equation change if the filling rate was different, say 80 gallons per hour?
  3. How can you calculate the total amount of water after 5 hours?
  4. What would the equation look like if the pool initially had no water in it?
  5. How does this equation relate to the concept of slope in linear functions?

Tip: In linear equations like this one, the coefficient of the variable (here 60) often represents the rate of change.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Rates of Change

Formulas

y = mx + b (Linear Equation)

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 7-8