The sum of two numbers is nine. Four times the smaller is equal to two times the larger.
1 + 8
2 + 7
3 + 6
4 + 5
Which of those meets the other criteria?
To solve this problem, let's assume the two numbers as variables. Let's call the smaller number "x" and the larger number "y".
According to the problem, the sum of the two numbers is nine, so we can write the equation:
x + y = 9 (Equation 1)
The problem also states that four times the smaller number is equal to two times the larger number. Mathematically, this can be expressed as:
4x = 2y
To simplify this equation, divide both sides by 2:
2x = y (Equation 2)
Now we have a system of two equations: Equation 1 and Equation 2. We can solve this system by substitution or elimination method.
Substitution Method:
In Equation 1, we can solve for y in terms of x:
y = 9 - x
Now substitute this value of y into Equation 2:
2x = 9 - x
Simplify the equation:
3x = 9
Divide both sides by 3:
x = 3
Now substitute this value of x back into Equation 1:
3 + y = 9
Simplify the equation:
y = 6
So, the smaller number x is 3 and the larger number y is 6.