A number is 8 more than another number.If the product of the two numbers is 20.Find the numbers.
Let's call the first number "x" and the second number "y".
According to the given information:
1) The first number is 8 more than the second number, so we can write the equation: x = y + 8.
2) The product of the two numbers is 20, so we can write the equation: x * y = 20.
Now we have a system of two equations:
Equation 1: x = y + 8
Equation 2: x * y = 20
We can substitute Equation 1 into Equation 2 to solve for y:
(y + 8) * y = 20
y^2 + 8y = 20
Rearranging the equation: y^2 + 8y - 20 = 0
We can factor this quadratic equation or use the quadratic formula to solve for y. Let's use the latter:
Using the quadratic formula: y = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 8, and c = -20.
y = (-8 ± √(8^2 - 4 * 1 * -20)) / (2 * 1)
y = (-8 ± √(64 + 80)) / 2
y = (-8 ± √144) / 2
y = (-8 ± 12) / 2
Now we have two possible values for y:
1) y = (-8 + 12) / 2 = 4 / 2 = 2
2) y = (-8 - 12) / 2 = -20 / 2 = -10
Now, we can substitute these values of y back into Equation 1 to find the corresponding values of x:
1) If y = 2, then x = y + 8 = 2 + 8 = 10.
2) If y = -10, then x = y + 8 = -10 + 8 = -2.
Therefore, the two numbers are 10 and -2.
To find the two numbers, let's set up a system of equations based on the given information.
Let's assume the first number is represented by 'x' and the second number is represented by 'y'.
We're given that a number is 8 more than another number, which can be expressed as:
x = y + 8 -- Equation 1
We're also told that the product of the two numbers is 20, which can be expressed as:
x * y = 20 -- Equation 2
Now, we have a system of equations:
Equation 1: x = y + 8
Equation 2: x * y = 20
To solve this system of equations, we can substitute Equation 1 into Equation 2, as follows:
(y + 8) * y = 20
Expanding and rearranging, we get:
y^2 + 8y = 20
Rearranging again, we have:
y^2 + 8y - 20 = 0
Now we can solve this quadratic equation for 'y' using factoring, completing the square, or the quadratic formula. Let's use factoring for this example.
We observe that the equation factors as:
(y + 10)(y - 2) = 0
Setting each factor equal to zero, we get two possible values for 'y':
y + 10 = 0 --> y = -10
y - 2 = 0 --> y = 2
So, we have two potential solutions for 'y': y = -10 or y = 2.
Substituting these values back into Equation 1, we can find the corresponding values of 'x':
For y = -10:
x = y + 8
x = -10 + 8
x = -2
For y = 2:
x = y + 8
x = 2 + 8
x = 10
Therefore, the two numbers are either (-2, -10) or (10, 2).
Easy to figure out by looking at the factors of 20
1x20
2x10
4x5
which have a difference of 8 ??
formal way:
let one number be x
let the other be x+8
x(x+8) = 20
x^2 + 8x - 20 = 0
(x+10)(x-2) = 0
x = -10 or x = 2
if x = 2, the numbers are 2 and 10
if x = -10, the number are -10 and -2