The admission ticket of an amusement park is $50 per head, and there is a 30% discount for a group of equal or over 30 people. What is the minimum size of a group that would rather buy the 30 people group tickets, as that is the cheaper option?
To find the minimum size of a group that would rather buy the 30 people group tickets, we need to compare the cost of individual tickets with the cost of group tickets. Let's break down the calculations step by step:
1. Calculate the cost of individual tickets:
- The admission ticket of the amusement park is $50 per head.
2. Calculate the cost of group tickets with the discount:
- The group discount is 30% for a group of equal or over 30 people.
- To calculate the cost of group tickets, we need to apply the discount to the individual ticket price:
- 30% of $50 = 0.3 * $50 = $15 (discount per ticket)
- Cost per ticket with discount = $50 - $15 = $35
- So, the cost of group tickets for each person is $35.
3. Compare the cost of individual tickets with the cost of group tickets:
- If the cost of group tickets is less than the cost of individual tickets, it would be better to choose the group tickets for groups of that size or larger.
- Let's assume we have a group of n people. The cost of individual tickets for n people is n * $50.
- The cost of group tickets for n people is n * $35.
4. Set up an inequality to find the minimum value of n:
- n * $35 < n * $50
- Dividing both sides of the inequality by n (assuming n > 0):
- $35 < $50
- Since $35 is less than $50, this inequality will hold for any positive value of n.
- Therefore, any group size equal to or larger than 30 would be better off buying the group tickets.
So, the minimum size of a group that would rather buy the 30 people group tickets is 30.