A dad gave his 3 sons each the same amount of money in an envelope. He took $20 from one son for get

A dad gave his 3 sons each the same amount of money in an envelope. He took $20 from one son for getting a D on a math test and he gave another son an extra $35 for doing extra chores. Combined, the sons had $81. Figure out how much each son had.

Let x, y, and z be the money each son received.

To begin, x = y = z.

But then, Dad took 20 from son X and gave it to son Y.
So now, x = y - 20

Next, he gave Son Z an extra $35 for chores
So z is now y + 35 since y and z used to be equal

Combined, they all have 81.
x + y + z = 181

But with the changes, it is:
(y - 20) + y + (y + 35)

Combine like terms:
3y - 20 + 35 = 81
3y + 15 = 81

Subtract 15 from each side:
3y = 66

Divide each side by 3 to isolate y
y = 22

Since x = y - 20, x = 2

Since z = y + 35, we have z = 57

Checking our work, 2 + 22 + 57 = 81.