Question

The sum of two numbers is 24 and their product is 108
The first number is 12+x , find the other
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Answer 1

Solution:-

Given:-

The sum of two number is 24 :-

x + y =24

Their products is 108

xy = 108

One of the number is 12 + x

We get

12 + x + y = 24

x + y = 12 ........( i )

Now take

xy = 108

(12 + x )y = 108

12y + xy = 108

xy = 108 - 12y

x = 108/y - 12 .......... ( ii )

Now put the (ii) on (i)

108/y - 12 + y = 12

Now taking lcm

108 - 12y + y² = 12 y

y² - 24y + 108 = 0

Solve by factorization method

y² - 18y - 6y + 108 = 0

y ( y - 18 ) - 6 ( y - 18 )

(y - 6) ( y - 18 )

y = 6 , y = 18

When y = 6

x + y = 12

x + 6 = 12

x = 6

When y = 18

x + y = 12

x + 18 = 12

x = 12 - 18

x = - 6