The sum of two numbers is 12 whole number 2/3 of one of the numbers is equal to 1/3 of the other.find the two numbers
x+y = 12
(2/3)x = (1/3)y
times 3
2x = y
sub that into our first equation
x + y = 12
x + 2x = 12
3x = 12
x = 4
y = 8
The two numbers are 4 and 8
check:
is (2/3)(4) = (1/3)(8) ? YES
is (2/3)(8) = (1/3)(4) ? NO
So we have to take 2/3 of 4 and 1/3 of 8 to satisfy the 2nd condition.
that is,
(1/3)x = (2/3)y
x = 2y
2y + y = 12
..
y = 4, then x = 8
Well, well, well! It seems we have a math problem to solve and I'm here to clown around and help you out! Let's dive in, shall we?
Let's call our two numbers x and y, because I'm feeling extra creative today.
According to the problem, their sum is 12. So we can write our first equation as:
x + y = 12
Now, it's time for the next piece of the puzzle. The problem says that 2/3 of one number is equal to 1/3 of the other.
Mathematically speaking, we can express this as:
(2/3)x = (1/3)y
Now, my tiny mathematician friend, we have a system of equations to solve! Brace yourself!
We have:
x + y = 12
(2/3)x = (1/3)y
To make things easier, let's get rid of those pesky fractions. We can multiply both sides of the second equation by 3 to get rid of the fractions:
3 * (2/3)x = 3 * (1/3)y
2x = y
Now, we have a shiny new equation to work with:
x + y = 12
2x = y
Since we want to find the two numbers (x and y), we can do a fun little substitution!
We know that 2x = y, so we can substitute that into the first equation:
x + 2x = 12
3x = 12
x = 4
And now, my friend, the grand finale! To find y, we simply substitute our found value of x into one of the equations:
2x = y
2 * 4 = y
8 = y
Ta-da! Our two numbers are x = 4 and y = 8.
I hope you had as much fun as I did solving this math problem! Feel free to ask me anything else and I'll put on my clown nose and give you another laugh!
Let's assume the two numbers are x and y.
According to the problem, the sum of the two numbers is 12, so we can write the following equation:
x + y = 12 (Equation 1)
It is also given that 2/3 of one of the numbers is equal to 1/3 of the other. We can write this as:
2/3x = 1/3y
To simplify this equation, we can cross-multiply:
2y = 3x
Now, we have two equations:
x + y = 12 (Equation 1)
2y = 3x (Equation 2)
To solve these two equations simultaneously, we can use substitution or elimination method. Let's use the elimination method:
Multiply Equation 1 by 3 to eliminate x:
3x + 3y = 36 (Equation 3)
Now, subtract Equation 2 from Equation 3:
3x + 3y - 3x = 36 - 2y
Simplifying the equation:
3y - 2y = 36
y = 36
Now, substitute the value of y into Equation 1:
x + 36 = 12
x = 12 - 36
x = -24
So, the two numbers are -24 and 36.
To solve this problem, we can set up two equations based on the given information.
Let's assume the two numbers are represented by variables x and y.
According to the problem, the sum of the two numbers is 12:
Equation 1: x + y = 12
We are also told that 2/3 of one of the numbers is equal to 1/3 of the other:
Equation 2: (2/3)*x = (1/3)*y
To solve these equations, we can use substitution or elimination method.
Let's use substitution to solve the equations.
From Equation 2, we can write x in terms of y:
(2/3)*x = (1/3)*y
x = (1/3)*(3/2)*y
x = (1/2)*y
Now, substitute the value of x in Equation 1:
(1/2)*y + y = 12
(3/2)*y = 12
3y = 24
y = 8
Substitute the value of y back into Equation 1 to find x:
x + 8 = 12
x = 12 - 8
x = 4
Therefore, the two numbers are x = 4 and y = 8.