Question

What should be subtracted from each of 6, 18, 41 and 137 so that they become proportionate to

each other?​

Answer 1

When we subtract 1 from 6, 18, 41 and 137 they become proportionate to each other

Given:

6, 18, 41 and 137

To find:

What should be subtracted from each of 6, 18, 41 and 137 so that they become proportionate to each other.

Solution:

Let x is subtracted from each number so that they become proportionate to each other

After subtracting x from each number the resultant numbers are

(6-x), (18- x), (41-x) and (137-x)

After subtracting x from each number the resultant numbers are in proportion to each other

⇒ $\frac{(6 - x)}{(18 - x)} = \frac{(41-x)}{(137-x)}$  

⇒ (6 - x) (137 - x) = (41 - x)(18 - x)

⇒ 822 -137x -6x + x² = 738 - 18x - 41x + x²

⇒ 822 - 143x = 738 - 59x

⇒ 143x - 59x = 822 - 738

⇒ 84x = 84

⇒ x = 1

Therefore, when we subtract 1 from 6, 18, 41 and 137 they become proportionate to each other

#SPJ2

Answer 2

Answer:

The answer to the given question is the number that should be subtracted from 6,18,41 and 137 so that they become proportionate to each other is 1.

Step-by-step explanation:

Given :

The numbers given are 6,18,41 and 137.

To find :

The number that should be subtracted from these numbers to make them proportionate to each other

Solution :

Let x be the number that should be subtracted from each of the numbers so that they become proportionate to each other.

On subtracting x from each number, the resultant value will be

$(6 - x)(18 - x)(41 - x) \: and \: (137 - x)$

After subtracting x from each of the numbers, they are proportionate to each other.

we have to make them as a ratio

$\frac{(6 - x)}{(18 - x)} = \frac{(41 - x)}{(137 - x)}$

On cross-multiplying, we get the value as

$(6 - x)(137 - x) = (41 - x)(18 - x)$

Then on multiplying, the value will be

$822 - 137x - 6x + {x}^{2} = 738 - 18x - 41x + {x}^{2}$

On comparing the two sides, the like terms get simplified

$8 22 - 143x = 738 - 59x$

Taking the like terms on the same side,

$822 - 738 = 143x - 59x \\ 84x = 84$

The value multiplies on the left side and divides the value on the right side.

$x = \frac{84}{84} \\ x = 1$

The value of x is found to be 1.

Therefore, the number that should be subtracted from 6,18,41 and 137 so that they become proportionate to each other is 1.

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