Question 892109
x = the cost of the article.


the sale price with a gain of 7.5% is equal to 1.075*x


the sale price with a loss of 12.5% is equal to .875*x


your equation is 1.075*x = .875*x + 6


this means that the sale price with a gain of 7.5% is 6 more than the sale price with a loss of 12.5%.


solve for x in this equation and you will get x = 30.


when x = 30, you get:


1.075 * 30 = 32.25


.875 * 30 = 26.25


add 6 to 26.25 and you get 32.25


1.075 * x was derived as follows:


x + .075 * x = (1 + .075) * x = 1.075 * x


.875 * x was derived as follows:


x - .125 * x = (1 - .125) * x = .875 * x


the equation of 1.075 * x = .875 * x + 6 was solved as follows:


subtract .875 * x from both sides of the equation to get:


1.075 * x - .875 * x = 6


factor out the x to get:


(1.075 - .875) * x = 6


simplify to get:


.2 * x = 6


divide both sides of this equation to get x = 6 / .2


solve for x to get x = 30.