How large is the tract

Question

A tract of land is 1/3 woodland, 25% orchards and 1/4 pastureland and the remaining 30 acres are lakes. How large is the tract?

Answer 1

Let x = the tract size

 

Translate:

  "1/3     ...  25%   ...  1/4 ...  30 acres"    means

   (1/3)x  + (1/4)x  + (1/4)x  + 30   = x       [note: 25% is 1/4]

    4x       + 3x       +    3x    + 360  = 12x     [multiply by LCM=12 to get rid of fractions]

  10x + 360 = 12x             [collect terms]

     360 = 2x            [subtract 10x from both sides]

      180 = x             [divide both sides by 2]

Answer 2

According to the info, we know the following:

 

1/3 is woodland

1/4 is orchards (25%)

1/4 is pasture.

 

This leaves 1/6 for lakes, which encompasses 30 acres.

 

If 30 acres is 1/6 of the entire acreage, the total tract is 180 acres.