Question

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

Answer 1

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