Question

what number to 12, 22, 42,&72 so that the resulting number may be in proportion.

Answer 1

Hi dear...here is your answer....
..

let x be added to Terms...

1st number= 12 +x

I2nd number =22 + x

3rd number = 42 + x

4rt number = 72 + x

now.....


( 12 + x ): ( 22 + x ) :: ( 42 + x ) : ( 72 + x )

now,product of outer terms = product of middle term

( 12 + x ) (72 + x ) = ( 42 + x ) ( 22 + x )

12×72 + 12x + 72x + x² = 42×22 + 42x + 22x + x²

= + 864 + 84x + x² =924 + 64x +x²
84x - 64x + x ^2- x ^2 = 924−864

20 x =60
x = 60/20

x = 3.....

so we have to add 3 so that number will be proportional.
Hope it helped you!
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