SOLUTION: Ben is one more than two times as old as Denise. In 19 years the sum of their ages will be 126. How old is Ben now?

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Question 213177: Ben is one more than two times as old as Denise. In 19 years the sum of their ages will be 126. How old is Ben now?
Found 2 solutions by drj, MathTherapy:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Ben is one more than two times as old as Denise. In 19 years the sum of their ages will be 126. How old is Ben now?

Let n = Denise age

Let 2n = Ben's age

Then (n+19)+(2n+19)=126 since in 19 years the sum of their ages will be 126.

The following will now solve the above equation

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


YOUR ANSWER


  • This is an equation! Solutions: n=29.3333333333333.
  • Graphical form: Equation %28n%2B19%29%2B%282n%2B19%29=126 was fully solved.
  • Text form: (n+19)+(2n+19)=126 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+%28n%2B19%29%2B%282n%2B19%29=126+%29
    For tutors: simplify_cartoon( (n+19)+(2n+19)=126 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28n%2B19%29+%29%2B%282%2An%2B19%29=126.
Remove unneeded parentheses around terms highlight_red%28+n+%29,highlight_red%28+19+%29
It becomes highlight_green%28+n+%29%2Bhighlight_green%28+19+%29%2B%282%2An%2B19%29=126.
Look at n%2B19%2Bhighlight_red%28+%282%2An%2B19%29+%29=126.
Remove unneeded parentheses around terms highlight_red%28+2%2An+%29,highlight_red%28+19+%29
It becomes n%2B19%2Bhighlight_green%28+2%2An+%29%2Bhighlight_green%28+19+%29=126.
Look at n%2Bhighlight_red%28+19+%29%2B2%2An%2Bhighlight_red%28+19+%29=126.
Added fractions or integers together
It becomes n%2Bhighlight_green%28+38+%29%2B2%2An=126.
Look at n%2Bhighlight_red%28+38+%29%2B2%2An=126.
Moved 38 to the right of expression
It becomes n%2B2%2An%2Bhighlight_green%28+38+%29=126.
Look at highlight_red%28+n+%29%2Bhighlight_red%28+2%2An+%29%2B38=126.
Eliminated similar terms highlight_red%28+n+%29,highlight_red%28+2%2An+%29 replacing them with highlight_green%28+%281%2B2%29%2An+%29
It becomes highlight_green%28+%281%2B2%29%2An+%29%2B38=126.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+2+%29%29%2An%2B38=126.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2An%2B38=126.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2An+%29%2B38=126.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2An%2B38=126.
Look at 3%2An%2B38=highlight_red%28+126+%29.
Moved these terms to the left highlight_green%28+-126+%29
It becomes 3%2An%2B38-highlight_green%28+126+%29=0.
Look at 3%2An%2Bhighlight_red%28+38+%29-highlight_red%28+126+%29=0.
Added fractions or integers together
It becomes 3%2An%2Bhighlight_green%28+-88+%29=0.
Look at 3%2An%2Bhighlight_red%28+-88+%29=0.
Removed extra sign in front of -88
It becomes 3%2An-highlight_green%28+88+%29=0.
Look at highlight_red%28+3%2An-88+%29=0.
Solved linear equation highlight_red%28+3%2An-88=0+%29 equivalent to 3*n-88 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=29.3333333333333.

Universal Simplifier and Solver


Done!



So Denise is 29.333 years old which means Ben is 58.667 years old

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit
http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit
http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Ben is one more than two times as old as Denise. In 19 years the sum of their ages will be 126. How old is Ben now?

Let Denise's current age be D

Since Ben's age is one more than 2 times Denise's age, then Ben's current age is 2D + 1

In 19 years, Denise will be D + 19, and Ben will be (2D + 1 + 19), or 2D + 20

Since in 19 years, their ages will total 126, then we'll have:

D + 19 + 2D + 20 = 126

3D + 39 = 126

3D = 87

D+=+87%2F3+=+29 which means that D, or Denise's current age is 29

Therefore, Ben is currently highlight_green%2859%29 (2*29 + 1) years-old.