A bag contains tomatoes that are either green or red. The ratio of green tomatoes to red tomatoes in the bag is $$4$$ to $$3$$. When five green tomatoes and five red tomatoes are removed, the ratio becomes $$3$$ to $$2$$. How many red tomatoes were originally in the bag?

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Uniteasy Admin · Accepted Answer

Since the ratio of green tomatoes to red tomatoes in the bag is $$4$$ to $$3$$, the number of green and red tomatoes can be given 4n and 3n, respectively.  In this way, we can be sure that the green-to-red ratio is   
$$\dfrac{4n}{3n}=\dfrac{4}{3}    $$c
If n is determined,  the number of red tomatoes is determined.
When five green tomatoes and five red tomatoes are removed, the ratio becomes $$3$$ to $$2$$, we can build the following equation
$$\dfrac{4n-5}{3n-5} = \dfrac{3}{2}   $$c 
Cross-multiplying gives
$$2(4n-5)=3(3n-5)$$c
$$8n-10=9n-15$$c
Then
$$n = 5$$c
The number of red tomatoes is calculated as
$$3n=15$$c
So B is correct

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