Question

the height of a lake decreases by 20 in over a period of time. the height decreases by 5 in each week. the equation below to represent the situation: -20 ÷ (-5) = 4 which description best explains the meaning of 4 in the equation? a the new height of the water in the lake is 4 in. b the change in the height of the lake is 4 in. c the time it takes for the lake to decrease in height by 5 in is 4 weeks. d the time it takes for the lake to decrease in height by 20 in is 4 weeks.

Explanation:

The equation \(-20\div(-5) = 4\) is used to find the time it takes for the lake's height to decrease by \(20\) inches when it decreases by \(5\) inches each week. In division, \(\text{dividend}\div\text{divisor}=\text{quotient}\). Here, the dividend \(- 20\) represents the total decrease in height (\(20\) inches, negative because it's a decrease), the divisor \(-5\) represents the rate of decrease per week (\(5\) inches per week, negative because it's a decrease). The quotient \(4\) represents the number of weeks it takes for the total decrease of \(20\) inches to occur.

• Option A: The equation is not about the new height, so this is incorrect.
• Option B: The change in height is \(20\) inches (from the problem statement), not \(4\) inches, so this is incorrect.
• Option C: The rate of decrease is \(5\) inches per week, and the equation is for a \(20\) - inch decrease, not a \(5\) - inch decrease, so this is incorrect.
• Option D: Since \(\text{time}=\frac{\text{total decrease}}{\text{rate of decrease}}\), \(\frac{20}{5}=4\) weeks for a \(20\) - inch decrease at a rate of \(5\) inches per week. The negative signs in the equation \(-20\div(-5)\) just indicate direction (decrease), and the magnitude calculation \(\frac{20}{5}\) gives the time for the \(20\) - inch decrease.

Answer:

D. The time it takes for the lake to decrease in height by \(20\) in is \(4\) weeks.