The table shows the number of tickets sold and the profit made at a fundraiser.
| Tickets Sold | Profit |
|---|---|
| 2 | $ 18 |
| 4 | $ 36 |
| 6 | $ 54 |
| 8 | $ 72 |
Which describes the relationship between the number of tickets sold and the profit?
A. Each ticket sold yields $8 of profit.
B. Each ticket sold yields $9 of profit.
C. Each ticket sold yields $16 of profit.
D. Each ticket sold yields $18 of profit.
Answer (2)
Calculate the profit per ticket for each row: Profit / Tickets Sold.
Find that the profit per ticket is constant and equals to $9. - Conclude that each ticket sold yields $9 of profit.
The relationship between the number of tickets sold and the profit is: Each ticket sold yields $9 of profit.
Explanation
Understanding the Problem We are given a table that shows the number of tickets sold and the profit made at a fundraiser. We need to determine the relationship between the number of tickets sold and the profit.
Calculating Profit per Ticket To find the relationship, we can calculate the profit per ticket for each row in the table. The profit per ticket is calculated by dividing the profit by the number of tickets sold.
Profit per Ticket for 2 Tickets For 2 tickets sold, the profit is 18. S o , t h e p ro f i tp er t i c k e t i s \frac{18}{2} = 9 .
Profit per Ticket for 4 Tickets For 4 tickets sold, the profit is 36. S o , t h e p ro f i tp er t i c k e t i s \frac{36}{4} = 9 .
Profit per Ticket for 6 Tickets For 6 tickets sold, the profit is 54. S o , t h e p ro f i tp er t i c k e t i s \frac{54}{6} = 9 .
Profit per Ticket for 8 Tickets For 8 tickets sold, the profit is 72. S o , t h e p ro f i tp er t i c k e t i s \frac{72}{8} = 9 .
Determining the Relationship Since the profit per ticket is the same for all rows, the relationship is linear and the profit per ticket is constant. The profit per ticket is $9. Therefore, each ticket sold yields $9 of profit.
Final Answer The relationship between the number of tickets sold and the profit is that each ticket sold yields $9 of profit.
Examples
Understanding proportional relationships is useful in many real-life situations. For example, if you are selling lemonade for $1.50 a cup, you can easily calculate your total earnings based on the number of cups you sell. If you sell 10 cups, you earn $1.50 \times 10 = $15. If you sell 25 cups, you earn $1.50 \times 25 = $37.50. This direct relationship helps in budgeting and forecasting income.
Each ticket sold at the fundraiser yields a consistent profit of $9. This was determined by calculating the profit per ticket for several quantities sold. Therefore, the correct choice is: each ticket sold yields $9 of profit.
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