Question

The product of two numbers is 1575 and their quotient is 9/7 find the number

Answer 1

Given ;-

⇒ Product of two numbers = 1572

⇒Quotient of the number = 9 / 7


TO FIND ;-

⇒ What is the number = ?


SOL ;-

⇒ It is given that product of two number is 1575,

⇒  so let us take the first number as x and the second number as y


                         ⇒Therefore we get as =  x × y = 1575



Similarly it is also given that , their  quotient is 9 / 7


                       ⇒ so we get as ,  x / y =  9 / 7.

                                         (  or )

                                       x =  9 y / 7


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⇒ Now , let us find the solution -


⇒  ( 9 y / 7 )  × y     =   1575

⇒            y²            =  ( 7 / 9 ) × 1575  

⇒           y²             =    1225

⇒           y              =     √1225

⇒          y              =     35


so , y = + / - 35 because we don''t know whether it is positive or negative


Now let us find the other number - 

                       x = 1575 / y
                       
                      x = 1575/35

                      x = 45.


⇒Therefore the another number is + / - 45



Therefore, the two numbers are -
           
  

                            ⇒ ( 35 , 45 )

                            ⇒ ( - 35 , - 45 )

Answer 2

So x*y = 1575 and x/y = 9/7. So x = 9y/7 and thus


(9y/7)*y = 1575 ---> y^2 = (7/9)*1575 = 1225 ---> y = +/- 35.

If y = 35, then x = 1575/35 = 45. If y = -35, then x = -45.

So there are two solution sets, namely {45, 35} and {-45, -35).