One number is eight more than twice another. If their sum is decreased by nine, the result is fourteen. Find the numbers.
n = (8 + 2 m)
n + m - 9 = 14
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(8 + 2 m) + m = 23
8 + 3 m = 23
3 m = 15
m = 5
n = 18
Let's assume the first number is x and the second number is y.
We know that "One number is eight more than twice another," so we can write the equation x = 2y + 8.
The second piece of information is that "their sum is decreased by nine, the result is fourteen," which translates to (x + y) - 9 = 14.
To solve this system of equations, we will substitute the value of x from the first equation into the second equation.
Substituting x = 2y + 8 into (x + y) - 9 = 14:
((2y + 8) + y) - 9 = 14
(3y + 8) - 9 = 14
3y - 1 = 14
3y = 14 + 1
3y = 15
y = 15 / 3
y = 5
Now we substitute the value of y back into the first equation to find x:
x = 2y + 8
x = 2(5) + 8
x = 10 + 8
x = 18
Therefore, the numbers are x = 18 and y = 5.
To solve this problem, let's assume the first number is "x" and the second number is "y".
According to the given information, we know that "One number is eight more than twice another." This can be written as:
x = 2y + 8
We are also told that "their sum is decreased by nine, the result is fourteen." This can be written as:
(x + y) - 9 = 14
Now we have a system of two equations:
x = 2y + 8
(x + y) - 9 = 14
To solve this system of equations, we can use the second equation to express x in terms of y:
x = 23 - y
Substituting this expression for x into the first equation, we have:
23 - y = 2y + 8
Solving this equation for y:
23 - 8 = 2y + y
15 = 3y
y = 5
Now we can substitute the value of y back into the expression for x:
x = 2y + 8
x = 2(5) + 8
x = 18
Therefore, the two numbers are 18 and 5.