Question

Problem Solving with Integers While descending into a valley in a hot-air balloon, your elevation decreased by 500 feet from an elevation of \(-600\) feet ( 600 feet below sea level). What is your new elevation?

Short answer

Answer: The new elevation is -1100 feet below sea level.

Step-by-step solution

Analyze the given information

We are given the initial elevation of -600 feet (below sea level) and a decrease of 500 feet. We need to calculate the new elevation.

Subtract the decrease in elevation from the initial elevation

To find the new elevation, subtract the decrease of 500 feet from the initial elevation of \(-600\) feet: \((-600) - (500)\).

Rewrite the subtraction as addition

Remember that subtracting a positive number is the same as adding its opposite (negative). So, we can rewrite the expression: \((-600) - (500) = (-600) + (-500)\).

Add the two integers

Now we need to add (-600) and (-500). Since both numbers are negative, we add their absolute values and then take the negative of the result: \(|-600| = 600\) \(|-500| = 500\) \((-600) + (-500) = -(600+500) = -1100\)

Interpret the result

The new elevation is \(-1100\) feet, which means it is 1100 feet below sea level.