Question

For every 5 people who bought $9.75 tickets to the football game, 3 people bought $14.50 tickets. If each of 35 people bought a $9.75 ticket, how many people bought the more expensive ticket?

a) 10
b) 15
c) 20
d) 25

Answer 1

When solving for the number of people who bought the $14.50 tickets based on the 5:3 ratio with $9.75 tickets, the correct answer is 21, which does not match any of the given multiple choice options.

Step-by-step explanation:

The question asks to determine how many people bought the more expensive $14.50 football game tickets given that for every 5 people who bought $9.75 tickets, 3 people bought $14.50 tickets, and 35 people bought the $9.75 tickets. Given the ratio of 5:3 for $9.75 to $14.50 tickets, we can set up a proportion to find the number of people who bought the more expensive tickets. We calculate this as follows:

1. Express the known ratio of 9.75 tickets to 14.50 tickets as 5/3.
2. Set up a proportion using the known ratio and the given quantity of people who bought 9.75 tickets (35): (5 people/9.75 tickets) / (3 people/14.50 tickets) = (35 people/9.75 tickets) / (x people/14.50 tickets).
3. Solving for x gives us: (5/3) = (35/x), which leads to 5x = 105 (after cross-multiplication).
4. Dividing both sides by 5, we get x = 21.
5. Now we can see that if 35 people bought the 9.75 tickets, then 21 people bought the 14.50 tickets.

However, the answer choices do not include 21, indicating a possible mistake. But upon further consideration, we realize there has been a mistake in interpreting the sequence of events. The ratio provided is for every group of 5 and 3 ticket buyers combined, not for separate groups. Therefore, since 35 is a multiple of 5, we need to divide 35 by 5 to find how many groups of ticket buyers there are, and then multiply this by 3 to get the number of 14.50 ticket buyers.

1. Divide 35 (the number of $9.75 ticket buyers) by 5, the number of $9.75 ticket buyers per group, which gives us 7 groups.
2. Multiply these 7 groups by 3, the number of 14.50 ticket buyers per group, to get 21, the total number of 14.50 ticket buyers.

Thus, the number of people who bought the more expensive ticket is 21, which is not an available answer choice. There must be an error in the provided multiple choice options, as none match the correct answer.