Prob 1) An owner raises a $60 coat by 40% then reduces it by 40%.. When raised by 40% you multiply by 1 plus that.. so 60(1.4) = 84 Now when you reduce anything by a discount, you mult by that discount to get the discount amount.. 84(.4) = $33.60 discount.. so new price is 84-33.6 = $50.40 OR... another way .. preferred way... simply multiply the original price by (1-discount rate) to give you the new price so.. 84(1-.4) = 84(.6) = $50.40 just the same Once it is raised to 84, what discount must we apply to get it back to 60? I set it up like so.. 84(x) = 60.. but once we find x we need to subtract 1 from x to get the discount.. because same as above..original * (1-the discount rate) gives us the new price.. so to find the actual discount rate in this instance, we need to find x then subtract it from 1 to get the actual discount rate 60/84 = .714 or 71.4%.. so the discount rate is 1-.714 = .286 or 28.6%