Question

The number must be added to each numbers 8,21,13 31 to make the ratios of first two number equal to the last two number is

Answer 1

Let number =x be added to each Number
Now
First Number=8+x
Second Number=21+x
Third Number=13+x
Fourth Number=31+x

Ratio of First Two number
=8+x:21+x
Ratio of Last Two number
=13+x:31+x

Both are equal Means,
8+x:21+x=13+x:31+x
$\frac{8 + x}{21 + x} = \frac{13 + x}{31 + x} \\ = (8 + x)(31 + x) = (13 + x)(21 + x) \\ = 248 + 8x + 31x + {x}^{2} = 273 + 13x + 21x + {x}^{2} \\ = 248 + 39x + {x}^{2} = 273 + 34x + {x}^{2} \\ = 39x + {x}^{2} - 34x - {x}^{2} = 273 - 248 \\ = 5x = 25 \\ = x = \frac{25}{5} \\ x = 5$
Number=5 Must Be added
$\boxed{\mathbf{Number=5}}$

Answer 2

Answer:

Let number =x be added to each Number

Now

First Number=8+x

Second Number=21+x

Third Number=13+x

Fourth Number=31+x

Ratio of First Two number

=8+x:21+x

Ratio of Last Two number

=13+x:31+x

Both 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+x

8+x

=

31+x

13+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=

5

25

x=5

Number=5 Must Be added

\boxed{\mathbf{Number=5}}

Number=5

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