On a shopping trip, peter spent 1/3 of his money for a jacket and another $5 for a hat. if peter still had 1/2 of his money left, how much money did he have originally ? ?

He should have started with $30.

Let m be the amount of money he had

m - (1/3)m - 5 = (1/2)m
(2/3)m - 5 = (1/2)m
Subtract both sides by (1/2)m
(2/3 - 1/2)m - 5 = 0
(1/6)m - 5 = 0
Add both sides by 5
(1/6)m = 5
Multiply both sides by 6
m = 30

Peter started with 30 dollars.

Have an awesome day! :)