At a bargain store. tanya bought 5 items that each cost the same amount. tony bought 6 items that each cost the same amount, but each was $1.75 less than the items that tanya bought. both tanya and tony paid the same amount of money. what was the individual cost of each person's items? (a) write an equation. let x represent the cost of one of tanya's items. (b) solve the equation. show your work (c) check your solution. show your work (d) state the solution in complete sentences.

(A) For x representing the cost of one of Tanya's items, her total purchase cost 5x. The cost of one of Tony's items is then (x-1.75) and the total of Tony's purchase is 6(x-1.75). The problem statement tells us these are equal values. Your equation is ...

... 5x = 6(x -1.75)

(B) Subtract 5x, simplify and add the opposite of the constant.

... 5x -5x = 6x -6·1.75 -5x

... 0 = x -10.50

... 10.50 = x

(C) 5x = 5·10.50 = 52.50

... 6(x -1.75) = 6·8.75 = 52.50 . . . . . the two purchases are the same value

(D) The individual cost of Tanya's iterms was $10.50. The individual cost of Tony's items was $8.75.

polynomial long division gives you f(x) = 2/(x-4) + x - 1. a proof of this fact has been left to the reader.

clearly as x go to + or - infinity, 2/(x-4) approaches 0. the oblique asypmote is y = x-1 as that is all that is left