Question

The depth finder on a fishing boat gives readings that are within 5% of the actual water depth. when the depth finder reading is 250 feet, the actual water depth x lies within a range given by an inequality.

Answer 1

A range refers to the least and greatest amount with respect of a certain number. In this case, the number referred to is the actual water depth, denoted as x. The general equation would be:

Depth finder reading = Actual Water Depth +/- 0.05*Actual Water Depth
250 ft = x +/- 0.05x
250 ft = x(1 +/- 0.05)
x = 250/(1 +/- 0.05)

Solving the equation:
x = 250(1 + 0.05) = 262.5 ft
x = 250(1 - 0.05) = 237.5 ft

Hence, the actual depth is between the range 262.5 ft - 237.5 ft.