Final answer:
The direct variation equation representing the scenario is S = 70P, with S as sales and P as the number of attendees, obtained by dividing $7,840 in sales by 112 attendees to get $70 as the constant of variation.
Step-by-step explanation:
To find the direct variation equation that represents the scenario where sales at a baseball game vary directly with the number of people in attendance, we use the relationship sales = k × attendance, where k is the constant of variation. Given that with 112 people in attendance, the sales are $7,840, we calculate k by dividing sales by attendance, which is k = $7,840 / 112 = $70. The direct variation equation is therefore S = 70P, where S stands for sales and P stands for the number of people in attendance.