Question

The sum of the 2 numbers is 45 and there product is 500

Answer 1

Answer:

Numbers are 25 and 20

Step-by-step explanation:

x+y=45

hence x=45-y

Also given

xy= 500

$(45 - y) \times y = 500$

${y }^{2} - 45y + 500 = 0$

$(y - 25)(y - 20) = 0$

y= 25 or 20

Answer 2

Let the two numbers be x and y

So,

x + y = 45

=> y = 45 - x ........(1)

Also,

xy = 500

=> x(45 - x) = 500

=> 45x - x^2 = 500

=> x^2 - 45x + 500 = 0

=> x^2 - 20x - 25x + 500 = 0

> x(x-20)-25(x-20) = 0

=> (x-20)(x-25) = 0

For, (x-20)(x-25) to be zero,

Either, x - 20 = 0 => x = 20

Or, x - 25 = 0 => x = 25

So, here we get two values of x

x = 20 or 25

when x = 20;

y = 45 - 20 = 25

When x = 25;

y = 45 - 25 = 20

So, the two possible sets of numbers are:

Either, x = 25 and

y = 20

Or, x = 20 and

y = 25

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