Priya, Mai, and Lin went to a cafe on a weekend. Their shared bill came to $25. Each student gave the server a $10 bill. The server took this $30 and brought back five $1 bills in change. Each student took $1 back, leaving the rest, $2, as a tip for the server.
As she walked away from the cafe, Lin thought, “Wait—this doesn’t make sense. Since I put in $10 and got $1 back, I wound up paying $9. So did Mai and Priya. Together, we paid $27. Then we left a $2 tip. That makes $29 total. And yet we originally gave the waiter $30. Where did the extra dollar go?”
Think about the situation and about Lin’s question. Do you agree that the numbers didn’t add up properly? Explain your reasoning.
this is an old old illusion.
There is no missing dollar.
Since they each got a dollar back, they only spent $27 altogether.
The bill was $25, and the waiter got $2.
Based on the situation described, it appears that there is a misconception in the way the numbers are being calculated. The error lies in combining the $27 paid by the students with the $2 tip to get a total of $29 and then trying to account for the missing extra dollar.
To understand the discrepancy, let's break down the situation step by step:
1. The bill at the cafe was $25.
2. Each student gave the server a $10 bill, so the server received a total of $30.
3. The server returned $5 in change, consisting of five $1 bills. The students each took $1 back from their change, so they effectively paid $9 each for the bill.
4. Since there are three students, their total payment for the bill was $9 x 3 = $27.
5. Additionally, they left a $2 tip for the server.
The mistake in the reasoning comes from trying to combine the $27 and the $2 tip to get a total of $29. This is incorrect because the tip is already included in the $27. Adding the $2 tip back to the $27 payment would mean double-counting the tip.
To clarify the calculation, we should focus on the amount actually paid for the bill, which is $27. There is no need to add the tip to this amount, as it has already been accounted for. Thus, there is no missing dollar to be found.
In summary, the numbers do add up properly. The mistake lies in misinterpreting the payment and tip amounts, leading to an inaccurate conclusion about the missing dollar.
Let's analyze the situation and the numbers to understand whether or not they add up properly.
At the start, the total bill was $25. Each of the three students gave $10, which makes a total of $30. The server brought back $5 in change.
Now, let's focus on the remaining $25 (bill) - $5 (change) = $20.
If each student took back $1, it means they have received a total of 3 * $1 = $3 back.
So, the total amount paid by the students should be $20 (remaining bill) + $3 (change) = $23, not $27.
The $27 that Lin mentioned includes the $2 tip they left for the server. However, you cannot add the tip to the $23 paid by the students because that amount was already part of the $23.
Therefore, there is no missing dollar. The error in Lin's reasoning lies in adding the tip amount again when calculating the total amount paid by the students.
In conclusion, the numbers do add up properly, and Lin's confusion arises from an incorrect calculation. The total amount paid by the students is $23 ($20 cash + $3 change), and the additional $2 is the tip they left for the server.