Question

what number must be subtracted from each of the number 10 12 19 24 to get the number which are in proportion?

Answer 1

To numbers to be in proportion

(10-x) / (12-x) = (19-x)/(24-x)

(10-x)(24-x) = (12-x)(19-x)

240 - 10x - 24x + x squared = 228 - 12x - 19x + x squared

240-34x = 228 -31x

12 = 3x

x = 4

Answer: 4 must be subtracted from each of the number.

Answer 2

4 must be subtracted from each of the number 10 , 12 , 19 , 24 to get the number which are in proportion

Given :

The numbers 10 , 12 , 19 , 24

To find :

The number must be subtracted from each of the number 10 , 12 , 19 , 24 to get the number which are in proportion

Solution :

Step 1 of 2 :

Form the equation

Here the given numbers are 10 , 12 , 19 , 24

Let x must be subtracted from each of the number 10 , 12 , 19 , 24 to get the number which are in proportion

By the given condition

$\displaystyle \sf{(10 - x) : (12 - x) =(19- x) : (24 - x) }$

Step 2 of 2 :

Find the number

$\displaystyle \sf{(10 - x) : (12 - x) =(19- x) : (24 - x) }$

$\displaystyle \sf{ \implies \frac{10 - x}{12 - x} = \frac{19 - x}{24 - x} }$

$\displaystyle \sf{ \implies (10 - x)(24 - x) = (19 - x)(12 - x)}$

$\displaystyle \sf{ \implies 240 - 10x - 24x + {x}^{2} = 228 - 12x - 19x + {x}^{2} }$

$\displaystyle \sf{ \implies 240 - 34x = 228 - 31x }$

$\displaystyle \sf{ \implies - 34x + 31x = 228 - 240 }$

$\displaystyle \sf{ \implies - 3x = - 12 }$

$\displaystyle \sf{ \implies x = 4}$

Hence 4 must be subtracted from each of the number 10 , 12 , 19 , 24 to get the number which are in proportion

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