SOLUTION: One number is eleven more than twice another. If their sum is decreased by nine, the result is seventeen. Find the numbers

Question 242805: One number is eleven more than twice another. If their sum is decreased by nine, the result is seventeen. Find the numbers
Found 2 solutions by unlockmath, oberobic:
Answer by unlockmath(1688) (Show Source): You can put this solution on YOUR website!
Hello,
Let's establish one number represented by x. The other number will be 2x+11 Then we can add these and subtract 9 to equal 17. Here's how it will look.
[(2x+11) + x] -9 = 17 Now we can combine like terms.
3x+2=17 Subtract 2 from both sides.
3x=15 Divide 3 into both sides.
x = 5
RJ Toftness
www.math-unlock.com
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
In the setup to the problem, always try to minimize the unknowns.
x = one number
It is 11 more than twice another number.
y = another number
x = 2y + 11
...
Now the second part says if the sum of x + y is decreased by 9 (that is: x + y - 9), the result is 17.
x + y - 9 = 17
Add 9 to both sides
x + y = 17+9 = 26
...
Now we have to solve x and y
...
Subtracting y from both sides of the equation above.
x + y - y = 26 - y
x = 26 - y
...
Substituting in the other equation.
x = 2y + 11
26 - y = 2y + 11
Adding y to both sides
26 = 3y + 11
Subtracting 11 from both sides
15 = 3y
Dividing both sides by 3
5 = y
...
y = 5
...
Recall
x + y = 26
Substituting for y
x + 5 = 26
Subtracting 5 from both sides
x = 21
Check your work (even if you're tired)...
Does x = 2y + 11?
21 = 2(5) + 11?
Yes it does.
Does x + y - 9 = 17?
21 + 5 - 9 = 17?
Yes it does.
So we're done.
x = 21
y = 5
RELATED QUESTIONS
One number is eleven more than twice another. If their sum is decreased by nine, the... (answered by jorel1380)
One number is fourteen more than twice another. If their sum is decreased by nine, the... (answered by checkley77)
One number is fourteen more than twice another. If their sum is decreased by nine, the... (answered by ewatrrr)
One number is nine more than twice another. If their sum is decreased by ten, the result... (answered by mananth,greenestamps,josgarithmetic)
One number is seven more than twice another. If their sum is decreased by nine, the... (answered by drj)
One number is eight more than twice another. If their sum is decreased by nine, the... (answered by nyc_function)
One number is fifteen more than twice another. If their sum is decreased by nine, the... (answered by ewatrrr)
One number is seven more than twice another. If their sum is decreased by nine, the... (answered by algebrahouse.com)
One number is nine more than twice another. If their sum is decreased by ten, the result... (answered by macston)