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

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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

Posted by

Deependra Verma

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