SOLUTION: The ages of four siblings equals 27. Peter is 2 years old then Paige. Perry is 3 years old then twice Paige, Pippa is 11 years younger than Perry. Find their ages

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Question 1010043: The ages of four siblings equals 27. Peter is 2 years old then Paige. Perry is 3 years old then twice Paige, Pippa is 11 years younger than Perry. Find their ages
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Peter's age
Let +b+ = Paige's age
Let +c+ = Perry's age
Let +d+ = Pippa's age
----------------------
There are 4 unknowns, so you
need 4 equations
(1) +a+%2B+b+%2B+c+%2B+d+=+27+
(2) +a+=+b+%2B+2+
(3) +c+=+2b+%2B+3+
(4) +d+=+c+-+11+
------------------
Substitute (3) into (4)
(4) +d+=+2b+%2B+3+-+11+
(4) +d+=+2b+-+8+
----------------------
Substitute (2), (3), and (4) into (1)
(1) +b+%2B+2+%2B+b+%2B+2b+%2B+3+%2B+2b+-+8+=+27+
(1) +6b+-+3+=+27+
(1) +6b+=+30+
(1) +b+=+5+
and
(2) +a+=+b+%2B+2+
(2) +a+=+5+%2B+2+
(2) +a+=+7+
and
(3) +c+=+2b+%2B+3+
(3) +c+=+2%2A5+%2B+3+
(3) +c+=+13+
and
(4) +d+=+c+-+11+
(4) +d+=+13+-+11+
(4) +d+=+2+
--------------------
Peter's age is 7
Paige's age is 5
Perry's age is 13
Pippa's age is 2
-----------------
check:
(1) +a+%2B+b+%2B+c+%2B+d+=+27+
(1) +7+%2B+5+%2B+13+%2B+2+=+27+
(1) +27+=+27+
OK
You can check the other 3 equations