SOLUTION: The sum of two numbers is 22 when the larger number is subtracted from three times the smaller the difference is 6 what are the two numbers

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: The sum of two numbers is 22 when the larger number is subtracted from three times the smaller the difference is 6 what are the two numbers      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 202006: The sum of two numbers is 22 when the larger number is subtracted from three times the smaller the difference is 6 what are the two numbers
Found 2 solutions by jim_thompson5910, RAY100:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"The sum of two numbers is 22" translates to x%2By=22

"the larger number is subtracted from three times the smaller the difference is 6" translates to 3x-y=6




Start with the given system of equations:
system%28x%2By=22%2C3x-y=6%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28x%2By%29%2B%283x-1y%29=%2822%29%2B%286%29


%281x%2B3x%29%2B%281y%2B-1y%29=22%2B6 Group like terms.


4x%2B0y=28 Combine like terms.


4x=28 Simplify.


x=%2828%29%2F%284%29 Divide both sides by 4 to isolate x.


x=7 Reduce.


------------------------------------------------------------------


x%2By=22 Now go back to the first equation.


7%2By=22 Plug in x=7.


7%2By=22 Multiply.


y=22-7 Subtract 7 from both sides.


y=15 Combine like terms on the right side.


So the solutions are x=7 and y=15.


So the larger number is 15 and the smaller number is 7.

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
(1) x+y=22
(2) 3x -y =6,,,,,,,x = smaller,,,y=larger
.
from (1) y=22-x
.
subst into (2),,,3x -(22-x) = 6
3x -22+x = 6
4x = 22+6=28
x=7.
.
y=22-x = 22-7 = 15
.
check,,,, (1) 7 + 15 = 22,,,,,ok
(2) 3(7) - 15 = 6,,,,,ok