Question

Each winter, a horse ranch gives sleigh rides. Tickets for adults are 510 each, and tickets for children are 56 each. No

more than 25 people can fit on the sleigh, and the ranch owners have a goal of eaming a minimum of $200 on each
ride. Write a system of inequalities to represent the situation.

Answer 1

To represent the situation with a system of inequalities, you would use a + c ≤ 25 to indicate the capacity constraint, 10a + 6c ≥ 200 for the earnings goal, along with a ≥ 0 and c ≥ 0 to ensure a non-negative number of tickets sold.

Step-by-step explanation:

The question involves creating a system of inequalities to represent the ticket sales and revenue for sleigh rides at a horse ranch. Let us denote the number of adult tickets by a and the number of children tickets by c.

The first inequality arises from the capacity constraint, which states that no more than 25 people can fit on the sleigh:
a + c ≤ 25

The second inequality comes from the earnings goal, requiring that the ranch earns a minimum of $200 per ride. At $10 per adult ticket and $6 per child ticket, this translates to:
10a + 6c ≥ 200

Finally, the fact that you cannot have negative numbers of passengers implies two more inequalities:
a ≥ 0
c ≥ 0