Portion formula

Question

Jay Miller sold his ski house at Attitash Mountain in New Hampshire for $298,000. This sale represented a loss of 18% off the original price. What was the original price Jay paid for the ski house? (Round your answer to the nearest dollar. Omit the "$" sign in your response.)

Answer 1

Hi Jay,

Instead of simply handing you an answer, how about I give you a procedure you can plug into a calculator very quickly. Deal?

The wording of this questions is very important!
To rephrase the question, since the loss was 18%, 82% of what is $298,000?

Let me give you a short way or formula.

is/of = %/100

is = 298,000
0f = x
%= 82

298,000/x = 82/100
(cross multiply) 298000*100 = x*82
29,800,000 = 82x
363,414.63 = x

The original price of the ski house was $363,414 rounded to the nearest dollar.

Answer 2

Since the sale represented an 18% loss of the original price, this means that the house was sold for 82% of the original price ( 100% - 18% = 82%) 

let x represent the original price of the house, then 82% of x would equal the price the house was sold for ($298,000)

before you write out the equation convert the 82% into decimal form, to do this simply divide 82% by 100% .... 82% / 100% = 0.82

so, the equation would look like the following:  (0.82)x = 298,000   (divide both sides by 0.82 to find x)

   (0.82)x = 298,000           ===>          x = 363,414.63 ≈ 363,415

    0.82         0.82

thus, the original price of the house was $363,415