I am back : Some brain churners : 1)You have borrowed money from your friend George. But now, George wants his money back. So you go to your other friend Frank and he writes you a check for the amount you owe George. You make your way to the bank and give the check to the teller. He accidentally mixes up the dollars and cents (for example $20.76 would become $76.20).That mixup allows you to repay both friends and have $1 left over.How much did you borrow from each friend?I will tell ans

Let's break down this intriguing problem step by step. The scenario involves borrowing money from two friends, George and Frank, and a mix-up at the bank that leads to an unexpected outcome. To find out how much you borrowed from each friend, we can set up some equations based on the information provided.

Setting Up the Problem

First, let's define the amounts borrowed:

• x = amount borrowed from George
• y = amount borrowed from Frank

According to the problem, you borrowed x dollars from George and y dollars from Frank. Frank writes you a check for the amount you owe George, which means the check is for x dollars.

Understanding the Bank Mix-Up

When you deposit the check at the bank, the teller mistakenly switches the dollars and cents. This means if the check was for x dollars and y cents, it gets processed as y dollars and x cents. The total amount you receive can be expressed as:

Amount received = y + (x / 100)

Now, you use this amount to pay back both friends. After repaying George and Frank, you have $1 left over. Therefore, we can set up the following equation:

y + (x / 100) = x + y + 1

Formulating the Equations

From the above equation, we can simplify it:

• y + (x / 100) = x + y + 1
• Subtracting y from both sides gives:
• (x / 100) = x + 1

Now, let's rearrange this equation:

x / 100 - x = 1

Multiplying through by 100 to eliminate the fraction:

x - 100x = 100

This simplifies to:

-99x = 100

So:

x = -100 / -99 = 100 / 99

Finding the Amounts

Now, we can substitute this value back into our equations to find y. Since we know that the total amount you received from Frank's check was enough to pay both George and Frank with $1 left over, we can express y in terms of x:

y = x + 1

Substituting the value of x we found:

y = (100 / 99) + 1 = (100 / 99) + (99 / 99) = 199 / 99

Final Amounts

Thus, the amounts borrowed from each friend are:

• Amount borrowed from George: $100 / 99 (approximately $1.01)
• Amount borrowed from Frank: $199 / 99 (approximately $2.01)

In summary, you borrowed approximately $1.01 from George and $2.01 from Frank. The mix-up at the bank allowed you to repay both friends and still have $1 left over. This problem illustrates how careful attention to detail is crucial in financial transactions, as even a small mistake can lead to unexpected outcomes!