From each of two numbers, half the smaller is subtracted, making the larger 4 times as large as the smaller. What is the ratio of the numbers?

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From each of two given numbers, half the smaller number is subtracted. After such subtraction, the larger number is $4$ times as large as the smaller number. What is the ratio of the numbers?

A guidance about this problem is most welcome.

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Set L the larger number, s the smaller number, then you have $L-s/2$ and $s-s/2$ and you know the factor between the two