After school, Alan, Bala and Calvin went to buy snacks. They shared the bill equally. However, Calvin did not have enough money and had to ask his friends to pay for his share. The ratio of the amount of money Alan paid to the amount of money Bala paid at the cashier counter was 5:6. The next morning, Calvin returned his share of the bill to Alan and Bala. He paid Alan $9.

(a) How much was the bill?

(b) How much did Calvin pay Bala

sugabreaddoughman May 31, 2024

#1**+1 **

Let the money of the bill be x.

(a) From the problem, we know that \(\frac{x/3 + 9}{x/3 + (x/3-9)} = \frac{5}{6}\)

We just have to solve for x now.

\(\frac{x+27}{2x-27}=\frac{5}{6}\)

\(6x+162=10x-135 \\ 4x=297\\x=74.26\)

The total bill was $74.25

(b) We just have to work backwards now.

First off, we know at first, Calvin had to pay \(74.25/3 = 24.75\) dollars.

However, he then had 9 dollars paid for him, so we have \(24.75-9=15.75\).

Calvin had to pay Bala $15.75

Thanks! :)

NotThatSmart May 31, 2024