Give the step-by-step reasoning process and then the final answer. A bag has seven apples, eight oranges, and 15 mangoes. Luisa takes out two apples from the bag, and takes out twice as many oranges as apples as she took from the bag. She then takes out 2/3 the number of mangoes from the bag. What is the remaining number of fruits in the bag?
When Luisa takes out two apples from the bag, 7 apples - 2 apples = 5 apples remain in the bag. She also takes 2 apples * 2 oranges / apple = 4 oranges from the bag. The total number of oranges remaining in the bag is 8 oranges - 4 oranges = 4 oranges. Additionally, a total of 2 / 3 * 15 mangoes = 10 mangoes are also removed from the bag. The total number of mangoes remaining in the bag is 15 mangoes - 10 mangoes = 5 mangoes. The total number of fruits that Luisa left in the bag is 5 apples + 4 oranges + 5 mangoes = 14.
The final answer: 14.