Jim cash the paycheck and went shopping he spent 3/8 of it on a mower 2/5 of it on at chainsaw and 180 On Tools if he has 270 left how much was his paycheck worth

Declaration

Let the original amount of the paycheck be x

Equation

Paycheck - cost of mower - cost of chainsaw - 180 = 270

x - [ (3/8) x + (2/5) x + 180] = 270

Solve

Change 3/8 and 2/5 to a common denominator and add.

3*5/8*5 + 2*8/5*8 = 15/40 + 16/30 = 31/40

x - [ (31/40) x + 180] = 270 Remove the outer brackets

x - (31/40) x - 180 = 270 Evaluate the "x"s

40/40x - 31/40x - 180 = 270

9x/40 - 180 = 270 Add 180 to both sides

9x/40 = 180 + 270

9x/40 = 450 Multiply by 40

9x = 18000 Divide by 9

x = 18000/9

x = 2000

His paycheck was 2000 dollars.