Answer: 7
Step-by-step explanation:
To solve this problem, let's break it down step by step.
1. Let's assume the number of oranges in the bowl is "o" and the number of apples is "a".
2. After 6 oranges were eaten, the new number of oranges is "o - 6".
3. We are told that there are now 3 times as many apples as oranges. So we can write the equation: "a = 3(o - 6)".
4. After a short time, 11 apples are eaten, so the new number of apples is "a - 11".
5. We are also told that there are now 4 times as many oranges as apples. So we can write the equation: "o = 4(a - 11)".
6. Now we have a system of two equations with two variables. We can solve this system to find the values of "o" and "a".
Let's solve the system of equations:
From equation 3, we have: "a = 3o - 18".
Substituting this value of "a" into equation 4, we get: "o = 4(3o - 18) - 11".
Simplifying this equation, we have: "o = 12o - 72 - 11".
Combining like terms, we get: "o = 12o - 83".
Bringing all the "o" terms to one side, we have: "11o = 83".
Dividing both sides by 11, we get: "o = 7".
Therefore, the original number of oranges in the bowl was 7.