Direct Variation: Abe's Earnings

What is the relationship between the amount of money Abe earns and the number of hours he works?

A) They are directly proportional

B) They are inversely proportional

C) They are unrelated

D) They are random

Answer:

The amount of money Abe earns is directly proportional to the number of hours he works.

Reflecting on the relationship between the amount of money Abe earns and the number of hours he works, it is clear that they are directly proportional. This means that as the number of hours Abe works increases, the amount of money he earns also increases in a linear manner.

This concept is known as direct variation, where the two variables have a constant ratio between them. In Abe's case, his earnings vary directly with the number of hours he works. This can be seen from the given information where he earned $262.50 for the first 21 hours he worked.

To calculate Abe's earnings per hour, we divide the total earnings by the number of hours worked: $262.50 / 21 hours = $12.5 per hour. This hourly rate remains constant, illustrating the direct proportionality between his earnings and the hours worked.

Therefore, the more hours Abe works, the more money he will earn, following a direct variation pattern. Understanding this concept is crucial for solving problems like determining Abe's earnings for a specific number of hours worked, as seen in the provided scenario.