Question

The product of two natural numbers is 9222. If they differ by 19 then find out the sum of the number.
205 199 197 193 195

Answer 1

Answer:

193.

Step-by-step explanation:

Finding the prime factors of 9222:-

9222 = 2*3*29*53

2*53 - 3*29

= 106 - 87 = 19

So the 2 numbers are 87 and 106

The sum is 106 + 87

= 193.

Answer 2

Answer:

The sum of two numbers is 193.

Step-by-step explanation:

Given the product of two numbers = 9222

The difference between two numbers = 19

Let the numbers be x and y.

Then the product is given by

$x \times y =9222$    

Rewriting the expression,

$\implies x =\dfrac{9222}{y}$                                                              ...(1)

And the difference is given by  $x-y= 19$              ...(2)    

Substituting value of x from equation (1), we get

$\dfrac{9222}{y}-y= 19$

$\implies \dfrac{9222-y^{2} }{y}= 19$

$\implies9222-y^{2} = 19y$

$\implies y^{2} +19y-9222=0$

$\implies y^2 + 106y - 87y - 9222 = 0$

$\implies y(y + 106) - 87(y + 106) = 0$

$(y + 106)(y - 87) = 0$

Therefore, $y + 106 = 0 ~\mbox{or}~ y - 87 = 0$

$y =- 106 ~\mbox{or}~ y = 87$

y cannot be a negative integer therefore the value of y is 87.

Substituting the value of y equation (2),

$x - 87 = 19$

$\implies x = 19 + 87=106$

Thus, the sum of two numbers is x + y = 106 + 87 = 193.

Therefore, the sum of two numbers is 193.

So, the correct answer is option 4.

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