what must be deducted from each of the number 7,10,12,18 so that the resultant numbers are the proportion

Question

what must be deducted from each of the number 7,10,12,18 so that the resultant numbers are the proportion

Answer 1

Your question is very unclear, but I think you may be asking what number to subtract from each of these numbers so that the first two are related by the same proportion as the last two.

 

Call the number you'll be subtracting x. Then the proportion of the first two numbers (7-x)/(10-x) should be equal to the proportion of the second two numbers (12-x)/(18-x). Set up the equation, then cross-multiply and combine like terms to solve:

 

(7-x)/(10-x) = (12-x)/(18-x)

(7-x)(18-x) = (10-x)(12-x)

126 - 7x - 18x + x² = 120 - 10x - 12x + x²

126 - 25x + x² = 120 - 22x + x²

126 - 25x = 120 - 22x

6 - 25x = -22x

6 = 3x

2 = x

 

The number that must be deducted is 2.

 

That will give you (7-2) / (10-2) = 5/8 and (12-2) / (18-2) = 10/16 = 5/8, which are indeed equal.