Question

what must be added to each of the number 5,9,7,12 to get the numbers which are in proportion ?​

Answer 1

$\purple{\underbrace{\bf{Answer}}}$

3

$\red{\bf{step-by-step-explanation}}$

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

$8*15 = 12*10 \:120 = 120$

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

Answer 2

Answer:

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 = 1208∗15=12∗10120=120

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