Question

Find the number which when added to 2, 14, 37 and 133 make them proportionate to each other.


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Answer 1

Answer:

Step-by-step explanation:

let x be the number to be added

2+x:14+x   =   37+x:133+x

2+x/14+x   =   37+x/133+x

cross multiplication:

(2+x)*(133+x) = (37+x)*(14+x)

266+2x+133x+x^2   =   518+37x+14x+x^2  

266+135x         =    518+51x

84x  =   252

x = 3

Answer 2

3 is the number that must be added to make 2, 14, 37, and 133 proportionate to one another.

Step-by-step explanation:

Given the four terms:

t1 = 2

t2 = 14

t3 = 37

t4 = 133

Let the number added to each term be x. So,

(2 + x) : (14 + x) :: (37 + x) : (133 + x)

By solving the two equations, we get

⇒ (2 + x) * (133 + x) = (37 + x) * (14 + x)

⇒ 266 + 2x + 133x + x^2 = 518 + 37x + 14x + x^2

⇒ 266 + 135x + x^2 = 518 + 51x + x^2

⇒ 135x - 51x = 518 - 218 + x^2 - x^2

⇒ 84x  =   252

⇒ x = 252/84

∵ x = 3

Learn more: Proportional number

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