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Question

The sum of two numbers exceeds thrice the smaller by 3. If the difference between them is 5, find the numbers

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Solution

Let the larger number be x and the smaller be y.
Then the first condition says x+y3y=3.
The second condition gives xy=5.
Thus we get two equations
x2y=3 .... (1)
xy=5 .... (2)
Subtracting the equation (2) by (1), we get y=2.
Hence y=2.
This gives x=y+5=2+5=7.
Thus the larger number is 7 and the smaller is 2.

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