SOLUTION: Mr. Rosario bought some numbers of apples and oranges in a ratio of 2:3. He gave away 2/3 of the apples to his sister and 23 oranges to his brother. The ratio of number of apples

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Question 1139560: Mr. Rosario bought some numbers of apples and oranges in a ratio of 2:3.
He gave away 2/3 of the apples to his sister and 23 oranges to his brother.
The ratio of number of apples to the number of oranges that he has now is
3:2. How many apples did Mr. Rosario buy? I need help setting up the equation.
I can't seem to figure it out on my own. Thank you.

Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.
As the condition states, originally Mr. R has 2x apples and 3x oranges, where x is some unknown number.


After all transactions we have this equation to find x


    %282x%2A%281-2%2F3%29%29%2F%283x+-23%29 = 3%2F2.


It is the equation you asked for.


It is exact translation of the condition into the Math / (equation) form.


In this stage the setup is done.


You still can to simplify the equation


    %282x%2A%281%2F3%29%29%2F%283x-23%29 = 3%2F2,   or


    %282x%29%2F%283%2A%283x-23%29%29 = 3%2F2,


    %282x%29%2F%289x-69%29 = 3%2F2


    4x = 3*(9x-23).


At this point everything should be clear to you.


Since you did not ask to solve the problem, I leave it to you.

I just completed my part and answered your question.

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