percentage of a discount

Question

quote for 60 snow plows (including the 5.5% Ohio sales tax) is $157,085.30, which includes a discount. The original price per snow plow is $2,820 (excluding sales tax).

By what percent have the snow plows been discounted?

Answer 1

157,085.30 = 60(one snowplow price, discounted)(1.055) so one snowplow, discounted, cost $2481.60. The 1.055 multiplier incorporates Ohio sales tax applied to the transaction.  This is computed by dividing my equation by both 60 & by 1.055 in order to isolate the single snowplow price, discounted.

 

Per snowplow, the discount amounted to 2820 - 2481.60 = $338.40.

 

338.40 ÷ 2820 = 0.12 which is a 12% discount.

Answer 2

Do this in a series of steps. First, you have to calculate the quoted price of the snow plows without sales tax. Given that the tax rate is 5.5% (0.055), you must divide the quote by 1.055. Second, calculate the original cost of the snow plows without the discount, which is 60 x $2,820. Third, divide the non-taxed price of the quote (step 1) by the original total (step 2), and subtract the result from 1. Convert to a percentage, and you'll have the answer.