SOLUTION: Dorothy is 6 years older than Ricardo. The product of their present ages is twice what the product of their ages was 6 years ago. How old is Dorothy?

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Question 204731: Dorothy is 6 years older than Ricardo. The product of their present ages is twice what the product of their ages was 6 years ago. How old is Dorothy?
Answer by ichudov(507)   (Show Source): You can put this solution on YOUR website!
Let's say Dorothy age is d, Ricardo's age is r:

Replace d with r+6:
(r+6)*r = 2*(r+6-6)*(r-6)
Give this problem to my universal simplifier:
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: r=0,r=18.
  • Graphical form: Equation was fully solved.
  • Text form: (r+6)*r=2*(r+6-6)*(r-6) simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( (r+6)*r=2*(r+6-6)*(r-6) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION


Look at .
Added fractions or integers together
It becomes .

Look at .
Remove extraneous zero highlight_red%28+0+%29
It becomes .

Look at .
Remove unneeded parentheses around factor highlight_red%28+r+%29
It becomes .

Look at .
Moved these terms to the left highlight_green%28+-2%2Ar%2A%28r-6%29+%29
It becomes .

Look at .
Expanded term r by using associative property on %28r%2B6%29
It becomes .

Look at .
Reduce similar several occurrences of highlight_red%28+r+%29 to highlight_green%28+r%5E2+%29
It becomes .

Look at .
Expanded term -2%2Ar by using associative property on %28r-6%29
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
Reduce similar several occurrences of highlight_red%28+r+%29 to highlight_green%28+r%5E2+%29
It becomes .

Look at .
Eliminated similar terms highlight_red%28+r%5E2+%29,highlight_red%28+-2%2Ar%5E2+%29 replacing them with highlight_green%28+%281-2%29%2Ar%5E2+%29
It becomes .

Look at .
Eliminated similar terms highlight_red%28+r%2A6+%29,highlight_red%28+12%2Ar+%29 replacing them with highlight_green%28+%286%2B12%29%2Ar+%29
It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Added fractions or integers together
It becomes .

Look at .
Removed extra sign in front of -1
It becomes .

Look at .
Remove unneeded parentheses around factor highlight_red%28+1+%29
It becomes .

Look at .
Remove unneeded parentheses around factor highlight_red%28+18+%29
It becomes .

Look at .
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes .

Look at .
Equation highlight_red%28+-r%5E2%2B18%2Ar=0+%29 is a quadratic equation: -r^2+18*r =0, and has solutions 0,18
It becomes .
Result:
This is an equation! Solutions: r=0,r=18.

Universal Simplifier and Solver


Done!


We can dismiss r=0 answer because it is nonsensical, so we have, r=18. Since d=r+6, dorothy's age = 18+6 = 24.

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