the sum of two numbers is 6. one number is 2 times the other. find the number
a = first number
b = second number
The sum of two numbers is 6 mean:
a + b = 6
One number is 2 times the other mean:
a = 2 b
Replace a = 2 b in equation:
a + b = 6
2 b + b = 6
3 b = 6 Divide both sides by 3
b = 6 / 3 = 2
a = 2 b = 2 * 2 = 4
a = 4 and b = 2
To solve this problem, let's denote the two numbers as x and y.
According to the problem statement, the sum of two numbers is 6. We can write this as an equation:
x + y = 6 (Equation 1)
It is also given that one number is 2 times the other. So, we can write this relationship as:
x = 2y (Equation 2)
Now we have a system of two equations with two variables (x and y). To find the values of x and y, we can use substitution or elimination method.
Let's use the substitution method to solve this system of equations:
Substitute the value of x from Equation 2 into Equation 1:
2y + y = 6
Combine like terms:
3y = 6
Divide both sides of the equation by 3:
y = 2
Now substitute the value of y back into Equation 2 to find x:
x = 2y = 2(2) = 4
Hence, the two numbers are 4 and 2.
To find the numbers, we can set up a system of equations based on the given information.
Let's assume one number is x. Then the other number would be 2x, as stated in the problem.
According to the problem, the sum of the two numbers is 6. So, we can write the equation as:
x + 2x = 6
To solve the equation, we can combine like terms:
3x = 6
Now, isolate x by dividing both sides of the equation by 3:
3x/3 = 6/3
x = 2
So, one number is 2. To find the other number, substitute this value back into the equation:
2(2) = 4
Therefore, the two numbers are 2 and 4.