Michael always helps his parents look after their fruits stall during school vacation. The stall sells only apples and pears. The ratio of apples to pears is 2 : 7 at first. Then a total of 96 fruits are added. The apples becomes 2 times as many as the original quantity, and the pears becomes 3 times as many as the original quantity. How many apples are there in the end?
Question
Michael always helps his parents look after their fruits stall during school vacation. The stall sells only apples and pears. The ratio of apples to pears is 2 : 7 at first. Then a total of 96 fruits are added. The apples becomes 2 times as many as the original quantity, and the pears becomes 3 times as many as the original quantity. How many apples are there in the end?
Solution
Let's solve this step by step:
Step 1: Let's denote the original number of apples as 2x and the original number of pears as 7x.
Step 2: According to the problem, after adding 96 fruits, the number of apples becomes twice the original quantity and the number of pears becomes three times the original quantity. So, we can write this as: 2*(2x) + 3*(7x) = 96.
Step 3: Simplify the equation: 4x + 21x = 96.
Step 4: Combine like terms: 25x = 96.
Step 5: Solve for x: x = 96 / 25 = 3.84.
Step 6: Now, we know that the number of apples in the end is twice the original quantity, so the final number of apples is 2 * 2x = 4x.
Step 7: Substitute x = 3.84 into the equation: 4 * 3.84 = 15.36.
Since the number of apples must be an integer, we round 15.36 to the nearest whole number, which is 15.
So, there are 15 apples in the end.
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