Pedro, Avi, and Carol earned a total of $150 by washing cars. Each earned a different amount. They agreed to share their earnings equally. Pedro gave half of his money equally to Abi and Carol. But then Avi has too much, so he gave $10 each to Pedro and Carol. Finally, Carol gave Pedro $2, and they all had the same amount. How much did each earn originally?

Let P, A and C be the amounts that Pedro, Avi and Carol had respectively. Pedro giving half of his money equally to both Avi and Carol would mean the amount Avi has now is A + P/4 and the amount Carol now has is C + P/4. The amount Pedro has left is P/2. If Avi now had too much and gave $10 each to Pedro and Carol, he would lose $20 and now has A + P/4 - 20. Carol now has C + P/4 + 10. Pedro now has P/2 + 10. Finally, Carol gave Pedro $ 2 and is $ 2 short and now has C + P/4 + 10 - 2. Pedro now has P/2 + 10 + 2. They all now have equal amounts. Since there are three of them and the total amount is $150, each person now has $150/3 = $50.

So, we now now have 3 equations.

P/2 + 10 + 2 = 50

C + P/4 + 10 - 2 = 50

A + P/4 - 20 = 50.

We now solve each equation.

First, P/2 + 10 + 2 = 50

P/2 + 12 = 50

P/2 = 50 - 12 = 38

P = 2 × 38 = 76

Next,

C + P/4 + 10 - 2 = 50

C + 76/4 + 8 = 50

C + 19 + 8 = 50

C + 27 = 50

C = 50 - 27 = 23

Finally,

A + P/4 - 20 = 50.

A + 76/4 - 20 = 50

A + 19 - 20 = 50

A - 1 = 50

A = 50 + 1 = 51