The sum of three prime numbers is 100. The difference of two of them is 24. What are the numbers?

Answers (1)

Let the three Prime numbers be x,y,z
According to the question,
x+y+z=100...(1)
and
x-y=24...(2)
Now adding both the equations,we'll get
2x+z=124
z=124-2x...(3)
Now,subtracting the equation (1) from (2),we'll get,
2y+z=76
z=76-2y...(4)
Now if we closely observe the Equation number (3) and (4),we;ll see that z is an even number.
The only number that is both even and prime is 2.
So we get,
2x+2=124
2x=122
x=61
And
2y+2=76
2y=74
y=37
So the numbers are 2,37,61

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