I am thinking of two numbers.What will my number be if their sum is 5 and their product is 6?
2 and 3 just sort of popped into my mind.
Let x= first unknown
y= second unknown
X+Y = 5 equation 1
(X)*(Y) = 6 equation 2
FROM EQUATION 2
Y= 6/X ( substitute to equation 1)
SO Equation 1
X + (6/X) = 5
X=2
Substitute (X) to ant equation)
Y= 5-2 = 3
SO X= 2 AND Y= 3
If you are going to give a detailed solution, then you should not gloss over the critical part of your solution:
SO Equation 1
X + (6/X) = 5
X=2
or else you might just as well state the obvious solution at the beginning.
3 and 2
To find the two numbers, let's assign variables to represent them. Let's say the first number is 'x' and the second number is 'y'.
We are given two pieces of information. First, the sum of the two numbers is 5, which can be expressed as:
x + y = 5
Second, the product of the two numbers is 6, which can be expressed as:
x * y = 6
We now have a system of two equations:
Equation 1: x + y = 5
Equation 2: x * y = 6
Now, to solve the system of equations, we can use one of several methods, such as substitution or elimination. Let's use substitution:
From Equation 1, we can isolate one variable (let's choose 'x'):
x = 5 - y
Substitute this value of 'x' into Equation 2:
(5 - y) * y = 6
Expanding the equation gives us:
5y - y^2 = 6
Rearranging the equation, we have:
y^2 - 5y + 6 = 0
Now, we solve this quadratic equation. Factoring the equation gives us:
(y - 2)(y - 3) = 0
Setting each factor equal to zero, we find two possible values for 'y':
y - 2 = 0 or y - 3 = 0
If y - 2 = 0, then y = 2. If y - 3 = 0, then y = 3.
Substituting these values for 'y' back into Equation 1 will help us find the corresponding values for 'x'.
If y = 2:
x + 2 = 5 => x = 3
If y = 3:
x + 3 = 5 => x = 2
So, the two possible number combinations that satisfy the given conditions are (x,y) = (3,2) and (x,y) = (2,3).