Answer:
Julie received $134.4 when she cashed her paycheck .
Step-by-step explanation:
Let the amount of paycheck be x
She paid $10 to her brother
She then spent $30 on fuel for her car
So, She left with amount = x-40
Now She spent half of the remaining money on a new tent for camping
Spent on camping = 
Remaining = 
She bought a pair of running shoes for $29.45
So, Remaining = 
We are given that She had $17.75 left.
So, 

Hence Julie received $134.4 when she cashed her paycheck .