What number must be added to each of the number 5 ,12 , 11 , ,21 to get the numbers in proportion?

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Solution

Let the number to be added be x.

the numbers 5,11,12,21 will be 5+x,11+x,12+x,21+x

(5+x)/(11++x)=(12+x)/(21+x)

Cross multiplying

(5+x)(21+x)=(12+x)(11+x)

(a+b)(c+d)=ab+ad+bc+bd

105+26x+(x^2)=132+23x+(x^2)

26x-23x=132-105

3x=27

x=9

The answer is 9.

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