SOLUTION: kirra is two years older then reggie. reggie is six times as old as delia. the average of their ages is nine years and four months. how old is each of them?

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Question 213985This question is from textbook
: kirra is two years older then reggie. reggie is six times as old as delia. the average of their ages is nine years and four months. how old is each of them? This question is from textbook

Found 2 solutions by Earlsdon, drj:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let K = Kirra's age, R = Reggie's age, and D = Delia's age.
%28K%2BR%2BD%29%2F3+=+91%2F3
K = R+2 "Kirra is two years older than Reggie." Rewrite as K = R-2
R = 6D "Reggie is six times as old as Delia."
K+R+D can be expressed as:
%28%286D-2%29%2B6D%2BD%29%2F3+=+91%2F3 Simplify.
%2813D%2B2%29%2F3+=+91%2F3 Multiply both sides by 3.
13D%2B2+=+28 Subtract 2 from both sides.
13D+=+26 Divide by 13.
D+=+2
R+=+6D
R+=+6%282%29
R+=+12
K+=+R%2B2
K+=+12%2B2
K+=+14
Kirra is 14 years old, Reggie is 12 years old and Delia is 2 years old.

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Kirra is two years older then Reggie. Reggie is six times as old as Delia. the average of their ages is nine years and four months. how old is each of them?

Step 1. Let x be the age of Delia. Let 6x be the age of Reggie. Let 6x+2 be the age of Kirra

Step 2. Let Average ages be A=9%2B1%2F3=28%2F3 years where 4/12=1/3 (4 months = 1/3 year)

Step 3. A=28%2F3=%28x%2B6x%2B6x%2B2%29%2F3 or

28=13x%2B2

26=13x

x=2 Delia's age. Then

6x=12 Reggie's age

6x%2B2=14 Kirra's age

Step 4. ANSWER: Delia is 2 years old, Reggie is 12 years old and Kirra is 14 years old.

As a check the average is %282%2B12%2B14%29%2F3=28%2F3

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