Question 215265
Vivian is 5 years older than Carmen. When Vivian's age is doubled and then subtracted from four times Carmen's age, the result is Carmen's present age, increased by 10. How old is each?


Step 1.  Let x be Carmen's age and let x+5 be Vivian's age.


Step 2.  Let 2(x+5) be doubled Vivian's age and let 4x be 4 times Carmen's age.


Step 3.  Now translate "When Vivian's age is doubled and then subtracted from four times Carmen's age, the result is Carmen's present age, increased by 10." into an algebraic expression, given as:


{{{4x-2(x+5)=x+10}}}


*[invoke explain_simplification "4x-2(x+5)=x+10" ]


With x=20  , then x+5=25


Step 4.  ANSWER:  Carmen is 20 and Vivian is 25


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