SOLUTION: Maria is 3 years older than Paula. Paula is 3 times Danielle's age. If their three ages add up to be 59 this year, how old will each girl be in 3 years?

Algebra ->  Equations -> SOLUTION: Maria is 3 years older than Paula. Paula is 3 times Danielle's age. If their three ages add up to be 59 this year, how old will each girl be in 3 years?      Log On


   

Question 1091669: Maria is 3 years older than Paula. Paula is 3 times Danielle's age. If their three ages add up to be 59 this year, how old will each girl be in 3 years?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Maria's age now
Let +b+ = Paula's age now
Let +c+ = Danielle's age now
----------------------------------
(1) +a+=+b+%2B+3+
(2) +b+=+3c+
(3) +a+%2B+b+%2B+c+=+59+
-------------------------
(2) +c+=+%281%2F3%29%2Ab+
Plug (1) and (2) into (3)
(3) +b+%2B+3+%2B+b+%2B+%281%2F3%29%2Ab+=+59+
(3) +2b+%2B+%281%2F3%29%2Ab+=+56+
Multiply both sides by +3+
(3) +6b+%2B+b+=+168+
(3) +7b+=+168+
(3) +b+=+24+
and
(1) +a+=+24+%2B+3+
(1) +a+=+27+
and
(2) +c+=+%281%2F3%29%2A24+
(2) +c+=+8+
-------------------------
+a+%2B+3+=+30+
+b+%2B+3+=+27+
+c+%2B+3+=+11+
In 3 years:
Maria will be 30
Paula will be 27
Danielle will be 11