Question

A lake’s level dropped 3 3/4 inches for 21 days during a drought. A heavy rainstorm raised the level by 8.25 feet. Afterwards, the level dropped 9.5 inches per day for 4 days. Scientists want to determine if the water level increased. Use your knowledge of rational numbers to determine the change in water level.

a) Increased
b) Decreased
c) Stayed the same
d) Cannot be determined

Answer 1

After converting all measurements to inches, the lake's water level dropped by 78.75 inches, rose by 99 inches, and then dropped by another 38 inches. The overall change is a decrease of 17.75 inches, indicating that the water level decreased.

Step-by-step explanation:

To determine the change in the water level of a lake, we need to convert all measurements to the same unit and then calculate the total change. Since the measurements are given in inches and feet, we will convert feet to inches (1 foot = 12 inches).

• Initial drop: 3 3/4 inches for 21 days = 3.75 inches/day * 21 days = 78.75 inches
• Rise after rainstorm: 8.25 feet to inches = 8.25 * 12 = 99 inches
• Subsequent drop: 9.5 inches/day for 4 days = 9.5 inches/day * 4 days = 38 inches

Overall change = Rainstorm rise - Initial drop - Subsequent drop = 99 inches - 78.75 inches - 38 inches = -17.75 inches. This means the water level has decreased by 17.75 inches, so the answer is (b) decreased.