what 2 numbers has a sum of 15 and a product of 56

i know that its 7 and 8 but i don't know the number sentence for this one....please help...thanks

let the two numbers be x and y

then x+y = 15 and xy = 56

from the first: y = 15-x
into the 2nd:
x(15-x) = 56
15x - x^2 - 56 = 0
x^2 - 15x + 56 = 8
(x-7)(x-8) = 0
x = 7 or x = 8

if x=7, then y = 8
if x = 8 , then y = 7

thanks so much....

To find two numbers that have a sum of 15 and a product of 56, let's use algebra.

Let's assume the two numbers are x and y. We can set up two equations based on the given information:

Equation 1: x + y = 15
Equation 2: x * y = 56

Now, we can solve these equations simultaneously to find the values of x and y.

From Equation 1, we can rewrite it as x = 15 - y.

Substitute this expression for x in Equation 2:

(15 - y) * y = 56

Expanding the equation:

15y - y^2 = 56

Rearranging and setting the equation equal to zero:

y^2 - 15y + 56 = 0

Now, we can factor this quadratic equation:

(y - 7)(y - 8) = 0

Setting each factor equal to zero and solving for y:

y - 7 = 0 --> y = 7
y - 8 = 0 --> y = 8

So, the two possible values for y are 7 and 8.

Now, substitute these values back into Equation 1 to find the corresponding values for x:

For y = 7:
x + 7 = 15 --> x = 8

For y = 8:
x + 8 = 15 --> x = 7

Therefore, the two numbers that have a sum of 15 and a product of 56 are 7 and 8.