SOLUTION: the diffrence between two numbers is 11 when the larger number is added to two times the smaller the sum is 59 what are the two numbers
Algebra.Com
Question 202045: the diffrence between two numbers is 11 when the larger number is added to two times the smaller the sum is 59 what are the two numbers
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"the difference between two numbers is 11" means that
"the larger number is added to two times the smaller the sum is 59" tells us that
Start with the given system of equations:
Multiply the both sides of the first equation by 2.
Distribute and multiply.
So we have the new system of equations:
Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:
Group like terms.
Combine like terms.
Simplify.
Divide both sides by to isolate .
Reduce.
------------------------------------------------------------------
Now go back to the first equation.
Plug in .
Subtract from both sides.
Combine like terms on the right side.
Divide both sides by to isolate .
Reduce.
So the solutions are and .
Which form the ordered pair )
.
This means that the system is consistent and independent.
So the two numbers are 27 and 16.
RELATED QUESTIONS
the difference between two numbers is 120. when three times the larger number is added to (answered by nyc_function)
The difference between two numbers is 20. When three times the larger number is added to... (answered by TimothyLamb)
The diffrence between two numbers is -38. Two times the smaller number minus five times... (answered by checkley71)
One number is 14 more than another. When half of the smaller number is added to the... (answered by CubeyThePenguin)
the larger of two numbers is 17 more than the smaller. When added together, the sum of... (answered by ikleyn)
The sum between two numbers is 18. The larger number is two times larger than the... (answered by Fombitz,rfer)
one number is 25 times larger then another the diffrence of there reciprocals is three... (answered by mananth)
The sum of two numbers is 11. Ten times the smaller number minus 5 times the larger... (answered by swincher4391)
Three times a larger number added to 4 times a smaller number totals 24. When twice the... (answered by checkley77)