Amir and Chand had an average of $180. After Amir spent $73 and Chand received $38 from his mother, Amir had 1/4 as much money as Chand. How much does each boy have at first?

Answer 1

Let's say Amir had x dollars at first.

After spending $73, Amir had x - 73 dollars left.
Chand had 180 - x dollars at first.

After receiving $38 from his mother, Chand had 180 - x + 38 dollars.
According to the given information, Amir had 1/4 as much money as Chand after spending $73.

So we can write the equation:
x - 73 = 1/4(180 - x + 38)

Solving for x:
x - 73 = 1/4(218 - x)
x - 73 = 54.5 - 1/4x
x + 1/4x = 73 + 54.5
5/4x = 127.5
x = 5/4 * 127.5
x = 159.375

So, Amir had $159.375 at first.

Chand had 180 - 159.375 = $20.625 at first.