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Answer :
By creating and solving a system of equations from the provided conditions, the two numbers in question are identified as 11 and 14.
The student presents a system of equations that can be expressed as follows:
- 11x = 9 + 8y (Equation 1)
- x - 4 = {1}/{2}y (Equation 2)
From Equation 2, we can express y in terms of x:
- y = 2(x - 4)
Substitute y in Equation 1:
- 11x = 9 + 8[2(x - 4)]
- 11x = 9 + 16x - 64
- 5x = 55
- x = 11
Now, using x to find y:
- y = 2(11 - 4)
- y = 2(7)
- y = 14
Therefore, the two numbers are x = 11 and y = 14.
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