In this problem, a ticket seller sold 50 tickets in total. Adult tickets cost 8 yuan each, while child tickets cost 4 yuan each. The total revenue was 312 yuan. We need to find out how many adult tickets and how many child tickets were sold.
Let's solve this using the assumption method. First, we'll assume that all 50 tickets sold were child tickets. If that were true, the total revenue would be 50 tickets times 4 yuan per ticket, which equals 200 yuan. However, we know the actual revenue was 312 yuan. This means our assumption resulted in a difference of 112 yuan less than the actual revenue. This difference will help us determine how many adult tickets were actually sold.
Now, let's find the number of adult tickets. The price difference between an adult ticket and a child ticket is 8 yuan minus 4 yuan, which equals 4 yuan. This means each adult ticket contributes 4 yuan extra compared to a child ticket. Since our total extra revenue is 112 yuan, and each adult ticket contributes 4 yuan extra, we can divide 112 by 4 to find the number of adult tickets. This gives us 28 adult tickets.
Now that we know there are 28 adult tickets, we can find the number of child tickets. Since the total number of tickets sold is 50, we can subtract the number of adult tickets from the total. That's 50 minus 28, which equals 22. Therefore, there are 22 child tickets.
Let's verify our solution. We found that there are 28 adult tickets and 22 child tickets. For adult tickets, the revenue is 28 times 8 yuan, which equals 224 yuan. For child tickets, the revenue is 22 times 4 yuan, which equals 88 yuan. The total revenue is 224 plus 88, which equals 312 yuan, matching our given total. Also, the total number of tickets is 28 plus 22, which equals 50, matching the given total number of tickets. Therefore, our solution is correct: 28 adult tickets and 22 child tickets were sold.