Question

What number must be added to each of the numbers 5,9,17,27 to make the new numbers is proportion

Answer 1

let the number to be added be x.

the numbers 5,9,17,27 will be  5+x,9+x,17+x,27+x

therefore:  5+x   = 17+x
                 9+x      27+x

  (5+x(27+x) = (9+x)(17+x)

 153+9x+17x+x^2= 135+5x+27x+x^2
153+26x+x^2= 135+32x+x^2
minus x^2 from both sides  153+26x=135+32x  ....32x-26x=153-135
                                                                     .... 6x=18
                                                                     ....x= 3

Therefore the number to be added to each them to make proportional is 3

Answer 2

5,9,17,27 will be 5+x,9+x,17+x,27+x

therefore:  5+x=17+x

                 9+x =27+x

  (5+x(27+x) = (9+x)(17+x)

 153+9x+17x+x²= 135+5x+27x+x²

153+26x+x²= 135+32x+x²

  153+26x=135+32x 

32x-26x=153-135

                                                                     6x=18

                                                                     x= 6