Julie cashed a paycheck and repaired her brother $10 that she borrowed from him. she then spent $30 on fuel for her car and half of the remaining money on a new tent for camping. she bought a pair of running shoes for $29.45 and had $17.75 left. how much did julie receive when she cashed her paycheck.

Remark
She starts out with x
She spends 10 dollars paying back her brother (that's - 10)
She spends 30 dollars on fuel (that - 30)
She spends 1/2 what's left on a tent ( that's 1/2 (x - 10 - 30) )
She then spent 29.45  on running shoes. 1/2 (x - 10 - 30) + 29.45 is her expenditures.

After all that she has 17.75 left. 

Equation
x - 10 - 30 - 1/2(x - 10 - 30) - 29.45 = 17.75   

Solve
Begin by adding 29.95 to both sides. 
x - 10 - 30 - 1/2(x - 10 - 30)  = 17.75 + 29.45 
x -10 - 30 - 1/2(x - 10 - 30)  = 47.20  Add the like terms on the left.
x - 40 - 1/2(x - 40) = 47.20 Add 40 to both sides. Don't go inside the brackets.
x - 1/2x + 1/2 (40) = 87.20
1/2 x + 20 = 87.20                        Subtract 20 from both sides.
1/2 x = 67.20                                Multiply by 2
x = 134.40 

Her salary $134.40

s= salary

s = $10 + $30 + $1/2(s- 30 - 10) + $29.45 + $17.75

s = 10 + 30 + 0.5s - 15 - 5 + 29.45 + 17.75
s = 0.5s + 67.20
0.5s = 67.20
s = $134.40