Question

The product of two number is 24 their sum is 14, find the numbers.

Answer 1

Let the number be x and y

so,

x × y = 24.......1st equation

and,

x + y = 14

x = 14 - y .......2nd eqn

than,

( 14 - y) y = 24

14y - y² = 24

y²- 14y + 24 = 0

y² - 12y - 2y + 24 = 0

y( y - 12) - 2( y - 12) = 0

( y - 2) ( y - 12) = 0

y = 2 , 12

and ,

put value of y in 1st or 2nd eqn to find x

Answer 2

One number is 12 and the other is 2.

Given:

Product of two numbers = 24

Sum of two numbers = 14

To Find:

The two numbers

Solution:

Let the two numbers be x and y

Therefore, according to the question,

$\implies xy=24\hspace{20}(i)\\\\\implies x+y=14\hspace{20}(ii)$

From equation (ii)

$\implies y = 14-x$

Put the value of y in equation (i)

$\implies x(14-x)=24\\\\\implies 14x-x^2=24\\\\\implies x^2-14x+24=0\\\\\implies x^2-12x-2x+24=0\\\\\implies x(x-12)-(x-12)=0\\\\\implies (x-12)(x-2)=0\\\\\implies x=12 \hspace{5} or \hspace{5} x=2$

Now, put the value of x in the equation (i):

if x = 12 ; y = 24/12 = 2

fi x = 2 ; y = 24/2 = 12

Therefore one number is 12 and the other is 2.

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