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9. The number that must be added to each of the numbers 8, 21, 13 and 31 to make the ratioof first two numbers equal to the ratio of last​

Answer»

Let NUMBER =X be added to each NumberNowFirst Number=8+xSecond Number=21+xThird Number=13+xFourth Number=31+xRatio of First TWO number=8+x:21+xRatio of Last Two number=13+x:31+xBoth are equal Means,8+x:21+x=13+x:31+x\begin{gathered} \frac{8 + x}{21 + x} = \frac{13 + x}{31 + x} \\ = (8 + x)(31 + x) = (13 + x)(21 + x) \\ = 248 + 8x + 31x + {x}^{2} = 273 + 13x + 21x + {x}^{2} \\ = 248 + 39x + {x}^{2} = 273 + 34x + {x}^{2} \\ = 39x + {x}^{2} - 34x - {x}^{2} = 273 - 248 \\ = 5x = 25 \\ = x = \frac{25}{5} \\ x = 5\end{gathered} 21+x8+x = 31+x13+x =(8+x)(31+x)=(13+x)(21+x)=248+8x+31x+x 2 =273+13x+21x+x 2 =248+39x+x 2 =273+34x+x 2 =39x+x 2 −34x−x 2 =273−248=5x=25=x= 525 x=5 Number=5 Must Be added\boxed{\mathbf{Number=5}} Number=5


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