SOLUTION: Respected sir, plz solve my maths problem. 1] In ten years ,david will be four times as old as aaron.twenty years ago,david was twice as old as ellen,if david is seven years

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Question 214369: Respected sir,
plz solve my maths problem.
1] In ten years ,david will be four times as old as aaron.twenty years ago,david was twice as old as ellen,if david is seven years older than ellen,how old is aaron?
waiting for yur reply.
thank u.
Found 2 solutions by Theo, drj:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let d = david's age now.
let a = aaron's age now.
let e = ellen's age now.
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In ten years ,david will be four times as old as aaron.
d+10 = 4*(a+10) = 4a+40
d = 4a+30
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Twenty years ago,david was twice as old as ellen.
d-20 = 2*(e-20)
d-20 = 2e-40
d = 2e-20
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If david is seven years older than ellen,how old is aaron?
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d = e+7
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Since d = 2e-20 and d = e+7, then 2e-20 must equal e+7
Equation to solve is:
2e-20 = e+7
This results in e = 27
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Ellen's age is 27
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Since d = e+7, this means that David is 7 years older than Ellen which makes David = 34 years old.
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Since d = 4a+30, and d = 34, then we have:
34 = 4a+30
This results in a = 1
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David is 34 years old
Aaron is 1 year old
Ellen is 27 years old.
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In 10 years Aaron is 11 and Dave is 44.
4 * 11 = 44 so this part of the original equation is good.
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20 years ago, David was twice as old as Ellen.
34-20 = 14
27-20 = 7
14/7 = 2 so this part of the equation is good also.
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Answer to your question is:
Aaron is 1 year old.
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Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
In ten years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is seven years older than Ellen,how old is Aaron?

Step 1. Let x be the age of Aaron and let y be the age of David

Step 2. Let y+10=4(x+10) In ten years, David will be four times as old as Aaron.

Step 3. Let y-7 age of Ellen.

Step 4. y-20=2(y-7-20) Twenty years ago, David was twice as old as Ellen.

Step 5. Solve y in Step 4 and then Solve Step 2 to get age of Aaron.

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


YOUR ANSWER


  • This is an equation! Solutions: y=34.
  • Graphical form: Equation y-20=2%2A%28y-7-20%29 was fully solved.
  • Text form: y-20=2*(y-7-20) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+y-20=2%2A%28y-7-20%29+%29
    For tutors: simplify_cartoon( y-20=2*(y-7-20) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at y-20=2%2A%28y-highlight_red%28+7+%29-highlight_red%28+20+%29%29.
Added fractions or integers together
It becomes y-20=2%2A%28y%2Bhighlight_green%28+-27+%29%29.
Look at y-20=2%2A%28y%2Bhighlight_red%28+-27+%29%29.
Removed extra sign in front of -27
It becomes y-20=2%2A%28y-highlight_green%28+27+%29%29.
Look at y-20=highlight_red%28+2%2A%28y-27%29+%29.
Moved these terms to the left highlight_green%28+-2%2A%28y-27%29+%29
It becomes y-20-highlight_green%28+2%2A%28y-27%29+%29=0.
Look at y-highlight_red%28+20+%29-2%2A%28y-27%29=0.
Moved -20 to the right of expression
It becomes y-2%2A%28y-27%29-highlight_green%28+20+%29=0.
Look at y-highlight_red%28+2%2A%28y-27%29+%29-20=0.
Expanded term -2 by using associative property on %28y-27%29
It becomes y-highlight_green%28+2%2Ay+%29%2Bhighlight_green%28+2%2A27+%29-20=0.
Look at y-2%2Ay%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+27+%29-20=0.
Multiplied numerator integers
It becomes y-2%2Ay%2Bhighlight_green%28+54+%29-20=0.
Look at y-2%2Ay%2Bhighlight_red%28+54+%29-highlight_red%28+20+%29=0.
Added fractions or integers together
It becomes y-2%2Ay%2Bhighlight_green%28+34+%29=0.
Look at highlight_red%28+y+%29-highlight_red%28+2%2Ay+%29%2B34=0.
Eliminated similar terms highlight_red%28+y+%29,highlight_red%28+-2%2Ay+%29 replacing them with highlight_green%28+%281-2%29%2Ay+%29
It becomes highlight_green%28+%281-2%29%2Ay+%29%2B34=0.
Look at %28highlight_red%28+1+%29-highlight_red%28+2+%29%29%2Ay%2B34=0.
Added fractions or integers together
It becomes %28highlight_green%28+-1+%29%29%2Ay%2B34=0.
Look at %28highlight_red%28+-1+%29%29%2Ay%2B34=0.
Removed extra sign in front of -1
It becomes %28-highlight_green%28+1+%29%29%2Ay%2B34=0.
Look at highlight_red%28+%28-highlight_red%28+1+%29%29%2Ay+%29%2B34=0.
Remove unneeded parentheses around factor highlight_red%28+1+%29
It becomes -highlight_green%28+1+%29%2Ay%2B34=0.
Look at -highlight_red%28+1+%29%2Ay%2B34=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -y%2B34=0.
Look at highlight_red%28+-y%2B34+%29=0.
Solved linear equation highlight_red%28+-y%2B34=0+%29 equivalent to -y+34 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: y=34.

Universal Simplifier and Solver


Done!



Step 6. Now that y is 34 years. Then

y%2B10=4%28x%2B10%29

34%2B10=4x%2B40

44=4x%2B40

44-40=4x

4=4x

1=x

Step 7. ANSWER is Aaron is one year old.

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