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?

Let the original number of green tomatoes be 4x and the original number of red tomatoes be 3x. After removing 5 of each, the new ratio is 4x minus 5 to 3x minus 5, which equals 3 to 2. Cross-multiplying gives 8x minus 10 equals 9x minus 15. Solving for x gives x equals 5, so the original number of red tomatoes is 3 multiplied by 5, which is 15.

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