The cost of a ticket to an amusement park is $42 per person for groups up to 8 people, the cost per ticket decreases by $3 for each person in the group. marcos's ticket cost $30. write and solve an equation to find the number of people in marcos's group.

For this case, the first thing we must do is define variables:
 x: number of people
 y: total cost of the ticket
 We write then the linear equation that represents this problem:
 y = (- 3/8) x + 42
 For y = 30 we have:
 30 = (- 3/8) x + 42
 We clear the value of x:
 (3/8) x = 42 - 30
 x = (8/3) * (12)
 x = 32
 
 the number of people in Marcos's group is:
 x = 32