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(52855)   (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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