Question

What number must be added to each of numbers 5,7,9,12 to get the number which are in proprotion

Answer 1

Answer:

Let the no. to be added be x.
then, the numbers will be 5+x , 9+x , 7+x and 12+x.
= 5+x : 9+x :: 7+x : 12+x
= (5+x)/(9+x) = (7+x)/(12+x)
=(5+x)(12+x) = (9+x)(7+x)               ( Do cross multiplication )
=(60+5x+12x+x square) = (63+9x+7x+x square)
=(60+17x+x square) = (63+16x+x square)
= 60+17x+x square = 63+16x+x square                           ( x square and x square gets cancelled )
= 60+17x = 63+16x
= 17x - 16x = 63 - 60
= x = 3                

Substitution 
The numbers are: 5+x , 9+x , 7+x and 12+x
5+3 , 9+3 , 7+3 , 12+3
8:12::10:15
Product of extremes = Product of means
8*15 = 12*10
120 = 120

 
Therefore 3 should be added to each of the numbers 5 , 9 , 7 and 12 to get the numbers which are in proportion.

I Hope It Will Help!
(^.^)

Answer 2

Answer:

3

Step-by-step explanation:

Let number to be added be x

(5+x)/(7+x) = (9+x)/(12+x)

=> 60 + 5x + 12x + x^2 = 63 + 9x + 7x + x^2

=> 17x - 16x = 3

=> x = 3