SOLUTION: THe sume of two numbers is 90. If 20 is added 3 times the smaller number, the result exceeds twice the larger number by 50. Let A represent the smaller number and let B represent t

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: THe sume of two numbers is 90. If 20 is added 3 times the smaller number, the result exceeds twice the larger number by 50. Let A represent the smaller number and let B represent t      Log On


   

Question 225337: THe sume of two numbers is 90. If 20 is added 3 times the smaller number, the result exceeds twice the larger number by 50. Let A represent the smaller number and let B represent the larger number.
a+b=90
Answer by LtAurora(115) About Me  (Show Source):
You can put this solution on YOUR website!
Our given equations are:
A%2BB=90
20%2B3A=2B%2B50
Solve the first one for a variable:
A=90-B
Plug this into the second equation:
20%2B3%2890-B%29=2B%2B50
Distribute the 3:
20%2B270-3B=2B%2B50
Combine like terms:
290-3B=2B%2B50
Move the -3B to the other side by adding it:
290=5B%2B50
Move the 50 over by subtracting it:
(((240=5B}}}
Divide both sides by 5:
B=48
Plug this back into our equation:
A=90-48
A=42
So, A=42 and B=48.