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) About Me  (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:V=C%2B5
--------------
From the second sentence:
4C-2V=C%2B10
Simplify:
Equation #2:3C-2V=10
--------------
Now you have 2 equations with 2 unknowns.
Substitute Equation #1 into Equation #2:
3C-2%28C%2B5%29=10
Solve for C:
3C-2C-10=10
highlight%28C=20%29
Next, plug this value of C into Equation #1 and solve for V:
highlight%28V=25%29
---------------
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) About Me  (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:

4x-2%28x%2B5%29=x%2B10

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


YOUR ANSWER


  • This is an equation! Solutions: x=20.
  • Graphical form: Equation 4x-2%2A%28x%2B5%29=x%2B10 was fully solved.
  • Text form: 4x-2*(x+5)=x+10 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4x-2%2A%28x%2B5%29=x%2B10+%29
    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 4%2Ax-2%2A%28x%2B5%29=highlight_red%28+x%2B10+%29.
Moved these terms to the left highlight_green%28+-x+%29,highlight_green%28+-10+%29
It becomes 4%2Ax-2%2A%28x%2B5%29-highlight_green%28+x+%29-highlight_green%28+10+%29=0.
Look at highlight_red%28+4%2Ax+%29-2%2A%28x%2B5%29-highlight_red%28+x+%29-10=0.
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 highlight_green%28+%284-1%29%2Ax+%29-2%2A%28x%2B5%29-10=0.
Look at %28highlight_red%28+4+%29-highlight_red%28+1+%29%29%2Ax-2%2A%28x%2B5%29-10=0.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2Ax-2%2A%28x%2B5%29-10=0.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2Ax+%29-2%2A%28x%2B5%29-10=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2Ax-2%2A%28x%2B5%29-10=0.
Look at 3%2Ax-highlight_red%28+2%2A%28x%2B5%29+%29-10=0.
Expanded term -2 by using associative property on %28x%2B5%29
It becomes 3%2Ax-highlight_green%28+2%2Ax+%29-highlight_green%28+2%2A5+%29-10=0.
Look at 3%2Ax-2%2Ax-highlight_red%28+2+%29%2Ahighlight_red%28+5+%29-10=0.
Multiplied numerator integers
It becomes 3%2Ax-2%2Ax-highlight_green%28+10+%29-10=0.
Look at 3%2Ax-2%2Ax-highlight_red%28+10+%29-highlight_red%28+10+%29=0.
Added fractions or integers together
It becomes 3%2Ax-2%2Ax%2Bhighlight_green%28+-20+%29=0.
Look at 3%2Ax-2%2Ax%2Bhighlight_red%28+-20+%29=0.
Removed extra sign in front of -20
It becomes 3%2Ax-2%2Ax-highlight_green%28+20+%29=0.
Look at highlight_red%28+3%2Ax+%29-highlight_red%28+2%2Ax+%29-20=0.
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 highlight_green%28+%283-2%29%2Ax+%29-20=0.
Look at highlight_red%28+%283-2%29+%29%2Ax-20=0.
Remove extraneous '1' from product highlight_red%28+%283-2%29+%29
It becomes x-20=0.
Look at highlight_red%28+x-20+%29=0.
Solved linear equation highlight_red%28+x-20=0+%29 equivalent to x-20 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
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