Mason 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 1 : 3 at first. Then a total of 30 fruits are added. The apples becomes 4 times as many as the original quantity, and the pears becomes 5 times as many as the original quantity. How many apples are there in the end?
Question
Mason 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 1 : 3 at first. Then a total of 30 fruits are added. The apples becomes 4 times as many as the original quantity, and the pears becomes 5 times as many as the original quantity. How many apples are there in the end?
Solution
Let's denote the initial number of apples as A and the initial number of pears as P.
From the problem, we know that the ratio of apples to pears is 1:3. This means that A:P = 1:3. So, we can say that P = 3A.
We also know that after 30 fruits are added, the number of apples becomes 4 times the original quantity and the number of pears becomes 5 times the original quantity. This can be written as:
A + 30 = 4A, P + 30 = 5P.
Substituting P = 3A into the second equation gives us:
3A + 30 = 5 * 3A, 3A + 30 = 15A.
Solving this equation for A gives us A = 2.5.
Substituting A = 2.5 into the first equation gives us:
2.5 + 30 = 4 * 2.5, 32.5 = 10.
So, there are 10 apples in the end.
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