Question 214774
Western State College is 18 years older than Southern State. Western is also 2.5 times as old as southern. How old is each? choices for southern state's age: 12,14,18


Step 1.  Let x be the age of Southern State, x+18 is the age of Western State College.


Step 2.  2.5x  Western age is also 2.5 times as old as southern.


Step 3.  x+18=2.5x as given by Steps 1 and 2.


Step 4.  Subtract x to both sides of the equation in Step 3


{{{x+18-x=2.5x-x}}}


{{{18=1.5x=3x/2}}}


Step 4.  Multiply 2/3 to both sides of the equation to get x


{{{(2/3)*18=(2/3)*(3/2)*x}}}


{{{12=x}}}


With x=12, then x+18=30 years old for Western


Step 5.  ANSWER:  Southern State's age is 12 years old and Western State's age is 30 years old.


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J