Problem 78 - Introductory Algebra for College Students

Question

Solve by writing a sum of signed numbers and adding. The water level of a reservoir is measured over a five-month period. At the beginning, the level is 20 feet. During this time, the level rose 3 feet, then fell 2 feet, then fell 1 foot, then fell 4 feet, and then rose 2 feet. What is the reservoir's water level at the end of the five months?

Step-by-Step Solution

Answer

The water level of the reservoir at the end of the five months is 18 feet.

Step 1: Establish Initial Water Level

The initial level of the reservoir is given in the exercise as 20 feet. So let's start with that number as our initial level.

Step 2: Account for the Changes

The changes in the water level over the five months are provided: a rise of 3 feet (which we treat as +3), a fall of 2 feet (treated as -2), a fall of 1 foot (treated as -1), a fall of 4 feet (treated as -4), and a rise of 2 feet (treated as +2). We need to sum these changes together.

Step 3: Calculate the Final Level

We sum all these changes and add them to the initial value to get the final water level. The operation is thus: \(20 + 3 - 2 - 1 - 4 + 2 \).