SOLUTION: Mr. Bins sold 1/2 of his farm to Mr. Frost and 100 acres to Mr. Slate. He now has 1/5 of his original farm land. How big was his farm originally? How much land does he have now

Algebra ->  Proportions  -> Lessons -> SOLUTION: Mr. Bins sold 1/2 of his farm to Mr. Frost and 100 acres to Mr. Slate. He now has 1/5 of his original farm land. How big was his farm originally? How much land does he have now      Log On


   

Question 1144699: Mr. Bins sold 1/2 of his farm to Mr. Frost and 100 acres to Mr. Slate. He now has 1/5 of his original farm land. How big was his farm originally? How much land does he have now?
Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the area of the farm originally.


Then from the condition you have this equation


    x%2F2 + 100 + x%2F5 = x.


To solve it, multiply both sides by 10. You will get


    5x + 1000 + 2x = 10x,


    1000 = 10x - 5x - 2x

    1000 = 3x

    x = 1000%2F3 acres.


It answers first question.


He has now 1%2F5 of  1000%2F3 acres, which is  200%2F3 acres.


It answers second question.


CHECK.  %281%2F2%29%2A%281000%2F3%29 + 100 + 200%2F3 = 1000%2F6+%2B+100+%2B+200%2F3 = 1000%2F6+%2B+600%2F6+%2B+400%2F6 = 2000%2F6 = 500%2F3 acres.   ! Correct !


Solved.