Question

Tony's Sandwich Shop earn the same $10 hourly wage. The formula for determining each employee's weekly earnings is e = r · h, where e is weekly earnings, r is the hourly rate of $10, and h is the number of hours worked. Which statement describes the relationship between e and h when r is replaced by 10?

A. The formula represents a direct proportion.
B. The formula represents an inverse proportion.
C. The formula represents neither a direct proportion nor an inverse proportion.
D. The formula represents both a direct proportion and an inverse proportion.

Answer 1

When r is replaced by 10 the formula represents a direct proportion. Thus the correct option is A.

Step-by-step explanation:

When the formula for weekly earnings (e = r * h) is used with r replaced by 10 (which is the hourly rate of $10), it simplifies to e = 10 * h. In a direct proportion, when one variable increases, the other also increases in a proportional manner. Here, as the number of hours worked (h) increases, the weekly earnings (e) increase proportionally at a rate of $10 per hour.

Hence, the relationship between e and h when r is replaced by 10 in the formula represents a direct proportion. This means that doubling the number of hours worked will double the weekly earnings, tripling the hours will triple the earnings, and so forth, maintaining a consistent proportional relationship.

This direct relationship implies that as the number of hours worked increases or decreases, the weekly earnings will adjust accordingly, consistently following a linear relationship with a fixed rate of $10 per hour. Therefore, the replacement of the hourly rate with a constant value of 10 in the formula solidifies the direct proportionality between weekly earnings and hours worked.

Therefore, the correct option is A.