SOLUTION: The total number of pears and oranges in a basket was 980. after a third of the pears and 230 oranges were sold, the ratio of pears to oranges left became 2:3. What was the ratio o

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Question 1163002: The total number of pears and oranges in a basket was 980. after a third of the pears and 230 oranges were sold, the ratio of pears to oranges left became 2:3. What was the ratio of pears to oranges at first??
Answer by ikleyn(52858)   (Show Source): You can put this solution on YOUR website!
.

Let x be one third of the number of pears initially.


Then the number of pears initially was 3x, and the number of oranges was 980-3x initially.


After one third of pears was sold, 3x-x = 2x pears remained.

After 230 oranges were sold, (980-3x)-230 = (750-3x) oranges remained.


From the condition, you have this equation


     = .


Equivalently,


    3*(2x) = 2*(750-3x),

    6x     = 1500 - 6x

    6x + 6x = 1500

    12x     = 1500

      x     =  = 125.


So, the number of pears originally was 3*125 = 375.

Hence, the number of oranges originally was  980 - 375 = 605,


and the ratio of pears to oranges initially was   = .    ANSWER

Solved.

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From my post, the major lesson to you is to learn on how I chose the major unknown.

I selected it in such a way to avoid working with fractions.



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