Finding original value based on an equal value

Question

The question is: An art curator was investigating the price trends of two art works that had the same initial value. The first painting, ‘Green poles’, doubled in value in the first year and then lost $8000 in the second year. In the third year its value was three quarters of the previous year. The second painting, ‘Orchids’, added $10 000 to its value in the first year then the second year its value was only a third of the previous year. In the third year its value improved to double that of the previous year. If the value of the paintings was the same in the third year, write an equation and solve it to find the initial value of each painting. The answer is $15200 and i don't understand how i get there or set it up.

Answer 1

PLZ learn how to make a table.

 

Let x = initial value of each painting       [note: "same initial value"]

 

 Painting      Initial     End First year        End Second year     End Third year Green p.          x                 2x                       2x - 8000            (3/4)(2x - 8000)

Orchids           x         (x + 10000)            (1/3)(x + 10000)       (2)((1/3)(x + 10000))

 

"value of the paintings was the same in the third year"    means     

(3/4)(2x - 8000)  =  (2)(1/3)(x + 10000)

(9)(2x + 8000) = (8)(x + 10000)     [multiply by LCM=12 to get rid of fractions]        18x - 72000 = 8x + 80000                 [distribute]          10x = 152000                            [add 72000 to both sides]            x = $15,200                              [divide both sides by 10]

 

Check:

Painting      Initial     End First year      End Second year     End Third year Green p.     $15,200      $30,400                $22,400                   $16,800 Orchids      $15,200      $25,200                  $8,400                   $16,800    Check -- the value is also the same at the end of the third year.

Answer 2

Gr, this took some thinking!

 

Let x be the original price of each, since it was the same.

 

The first year, Green Poles' value was 2x. Year two, it was 2x - 8000, and year three it was (3/4)(2x - 8000). You should be able to follow how I got there from the given information.

 

The year three value of Orchids is (2/3)(x + 10,000).

 

Since they are back to equal in year three...

 

(3/4)(2x - 8000) = (2/3)(x + 10,000)

 

Multiply each side by 12 to get rid of the fractions...

 

9(2x - 8000) = 8(x + 10,000)

18x - 72,000 = 8x + 80,000

10x = 152,000

x = 15,200

 

Boom.