Question

are the numbers 14 22 32 and 49 are in proportion if not what should be added to each of them so that the resulting numbers form a proportion
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Answer 1

Answer:

'2' should be added to each of them so that the resulting numbers form a proportion.

Step-by-step explanation:

Given numbers are $14, 22, 32, 49$

To check if the numbers are in proportion the ratios of corresponding numbers has to be equal.

Here, $\frac{14}{22}\neq \frac{32}{49}$

Hence this number are not in proportion.

Let $x$ be added to this number so that the resulting numbers becomes in proportion.

Resulting numbers will be,

$14+x, 22+x, 32+x, 49+x;$

Consider this numbers are in proportion,

∴      $\frac{14+x}{22+x}=\frac{32+x}{49+x}$

⇒   $(14+x)(49+x)=(32+x)(22+x)$

⇒   $14*49+14x+49x+x^{2} =32*22+32x+22x+x^{2}$

⇒   $686+63x+x^{2} =704+54x+x^{2}$

⇒   $(x^{2} +63x)-(x^{2}+54x)=704-686$

⇒   $x^{2} +63x-x^{2} -54x=18$

⇒   $9x=18$

⇒   $x=2$

Thus the resulting numbers will be, $14+2=16,22+2=24, 32+2=34, 49+2=51$

we can see, $\frac{16}{24}=\frac{34}{51}=\frac{2}{3}$

That is, numbers become in proportion.

Hence, 2 should be added to each of the numbers so that the resulting numbers form a proportion.