Question

what constant number must be added to each of 7,9,12,,15 to make them in proportion​

Answer 1

Given:

The numbers 7, 9, 12 and 15.

To Find:

The constant that must be added to these numbers to make them in proportion.

Solution:

Let's assume the unknown constant as x.

It is given that:

$\sf{\longrightarrow\:(7+x):(9+x)::(12+x):(15+x)}$

This means that:

$\sf{\longrightarrow\dfrac{7+x}{9+x}=\dfrac{12+x}{15+x}}$

Doing cross multiplication:

$\sf{\longrightarrow\:(7+x)(15+x)=(12+x)(9+x)}$

Solving:

$\sf{\longrightarrow\:105+7x+15x+x^2=108+12x+9x+x^2}$

$\sf{\longrightarrow\:105+22x=108+21x}$

$\sf{\longrightarrow\:22x-21x=108-105}$

$\sf{\longrightarrow\:x=3}$

This means that:

➡ 7 + 3 = 10

➡ 9 + 3 = 12

➡ 12 + 3 = 15

➡ 15 + 3 = 18

The proportion is:

10 : 12 :: 15 : 18

The constant to be added is 3.

Verification:

If the product of the means is equal to the product of the extremes, our answer is correct.

Means: 12 and 15

Extremes = 10 and 18

Product of means = Product of extremes

12 x 5 = 10 x 8

180 = 180

Hence verified and proved!