Question

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

Answer 1

let the 3 prime number be x, y ,z 
then 
x+y+z=100...(1)
and
x-y=24....(2)
adding (1) and (2)

2x+z=124
z=124-2x....(3)

subtracting (1) from (2)

2y+z=76
z=76-2y....(4)


From (3) and (4) we can see that z is even [ even - even = even, any number                                                                                      when multiplied by 2 gives even                                                                                       number]

The only number that is even and prime is '2'
so z =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