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.
