Question

A ticket brokering company is randomly distributing tickets to customers who pre-ordered tickets for an upcoming concert. Out of the first batch of tickets sent to pre-order customers, 20 are in row 7, 19 are in row 8, and 16 are in row 9. Which of the following is the best prediction of the number of tickets in row 7 in the next 33 tickets sent out?

Answer 1

Answer:

• 12 tickets

Explanation:

You must assume that the ratio of the number of tickets in row 7 is a constant.

That permits you to set a proportion with the ratio of the number of tickets in row 7 for the first batch of tickets and the ratio of the number of tickets in row 7 for the next 33 tickets sent out:

1. Ratio of number of tickets in row 7 for the first batch.

• Number of tickets in row 7: 20
• Total number of tickets: 20 + 19 + 16 = 55
• Ratio: 20/55

2. Ratio of number of tickets in row 7 in the next 33 tickets sent out:

• Number of tickets in row 7: x
• Total number of tickets sent out: 33
• Ratio: x/33

3. Proportion

Set the proportion and solve for x:

          $\dfrac{20}{55}=\dfrac{x}{33}\\\\\\20\times 33=55x\\\\\\ x=\dfrac{20\times 33}{55}\\ \\ \\ x=\dfrac{20\times 3}{5}\\ \\ \\ x=4\times 3\\ \\ \\ x=12$

Answer: 12 tickets