The amount of money that Sarah earns varies directly with the number of hours worked. If Sarah earns $320 for working 40 hours, determine the constant of proportionality.

per hour

1 answer

To find the constant of proportionality, we can use the formula for direct variation, which is:

\[ y = kx \]

where \( y \) is the amount of money earned, \( x \) is the number of hours worked, and \( k \) is the constant of proportionality (the earnings per hour).

From the problem, we know that Sarah earns $320 for working 40 hours. We can substitute these values into the formula:

\[ 320 = k \times 40 \]

To find \( k \), we can solve for it:

\[ k = \frac{320}{40} \]

Calculating this gives:

\[ k = 8 \]

Thus, the constant of proportionality, or Sarah's earnings per hour, is $8 per hour.