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.