SOLUTION: I would really appreciate anyone who would be willing to help me answer it! Vivian is 5 years older than Carmen. When Vivian's age is doubled and then subtracted from four times

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Question 215265: I would really appreciate anyone who would be willing to help me answer it!
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?
Found 2 solutions by tutor_paul, drj:
Answer by tutor_paul(519)   (Show Source): You can put this solution on YOUR website!
Write 2 Equations based on the information given. Let V=Vivian's age and C=Carmen's age:
From the first sentence:
Equation #1:
--------------
From the second sentence:

Simplify:
Equation #2:
--------------
Now you have 2 equations with 2 unknowns.
Substitute Equation #1 into Equation #2:

Solve for C:


Next, plug this value of C into Equation #1 and solve for V:

---------------
As a final check, plug these results back into Equation #1 and Equation #2 to be sure they still hold true. I'll leave that part to you.
===================
Good Luck,
tutor_paul@yahoo.com


Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
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:



Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=20.
  • Graphical form: Equation was fully solved.
  • Text form: 4x-2*(x+5)=x+10 simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( 4x-2*(x+5)=x+10 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Moved these terms to the left highlight_green%28+-x+%29,highlight_green%28+-10+%29
It becomes .
Look at .
Eliminated similar terms highlight_red%28+4%2Ax+%29,highlight_red%28+-x+%29 replacing them with highlight_green%28+%284-1%29%2Ax+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes .
Look at .
Expanded term -2 by using associative property on %28x%2B5%29
It becomes .
Look at .
Multiplied numerator integers
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Removed extra sign in front of -20
It becomes .
Look at .
Eliminated similar terms highlight_red%28+3%2Ax+%29,highlight_red%28+-2%2Ax+%29 replacing them with highlight_green%28+%283-2%29%2Ax+%29
It becomes .
Look at .
Remove extraneous '1' from product highlight_red%28+%283-2%29+%29
It becomes .
Look at .
Solved linear equation highlight_red%28+x-20=0+%29 equivalent to x-20 =0
It becomes .
Result:
This is an equation! Solutions: x=20.

Universal Simplifier and Solver


Done!



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




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