https://r2.erweima.ai/mathbot/image/1725453751683xg9bwsy2.jpg

Let's solve the problem presented in the image. The problem involves determining the price per ticket in a lottery so that the lottery operators can make a 40% profit.

### Step 1: Calculate the Total Prize Money
First, let's calculate the total amount of money that will be paid out in prizes:

- **$1,000,000 prize**: There is 1 prize of $1,000,000.
  \[
  1,000,000 \times 1 = 1,000,000
  \]
- **$50,000 prize**: There are 5 prizes of $50,000.
  \[
  50,000 \times 5 = 250,000
  \]
- **$1,000 prize**: There are 10 prizes of $1,000.
  \[
  1,000 \times 10 = 10,000
  \]
- **$50 prize**: There are 50 prizes of $50.
  \[
  50 \times 50 = 2,500
  \]

Adding these up gives us the total prize money:
\[
1,000,000 + 250,000 + 10,000 + 2,500 = 1,262,500
\]

### Step 2: Calculate the Total Revenue Needed
The lottery operators want to make a 40% profit. Let the cost per ticket be $ p $.

The total revenue generated by selling all 2,000,000 tickets will be:
\[
\text{Total Revenue} = 2,000,000 \times p
\]

The total cost, which includes the prize money, must be 60% of the total revenue (since the remaining 40% is the profit):
\[
1,262,500 = 0.6 \times (2,000,000 \times p)
\]

### Step 3: Solve for $ p $
Now, solve for $ p $ by rearranging the equation:
\[
p = \frac{1,262,500}{0.6 \times 2,000,000}
\]
\[
p = \frac{1,262,500}{1,200,000} \approx 1.05208
\]

Thus, the lottery operators should charge approximately **$1.05** per ticket to make a 40% profit.

---

Would you like further details on any part of this solution? Here are five related questions you might find interesting:

1. What would the price per ticket be if the lottery operators wanted a 50% profit?
2. How would the ticket price change if the number of total tickets was increased to 3 million?
3. What is the expected value of a single lottery ticket in this game?
4. How does the ticket price affect the total profit for the lottery operators?
5. What would happen to the ticket price if the total prize money increased by $100,000?

**Tip:** Understanding how expected value works in lottery games can help in making better decisions about participation in such games.

In a lottery, there are 2,000,000 tickets to be sold. The prizes are as follows: 1 prize of $1,000,000, 5 prizes of $50,000, 10 prizes of $1,000, and 50 prizes of $50. What should the lottery operators charge per ticket in order to make a 40% profit?

Learn how to determine the ticket price in a lottery where the total prize money is $1,262,500, and the operators want to make a 40% profit. This problem covers algebraic concepts like revenue and profit calculation, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation