SOLUTION: Hi jane is twice as old as carl and 4 times older than penny.owen is 2 years younger than penny. how old is jane when the total of their ages is 70. thanks

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Hi jane is twice as old as carl and 4 times older than penny.owen is 2 years younger than penny. how old is jane when the total of their ages is 70. thanks      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1018192: Hi
jane is twice as old as carl and 4 times older than penny.owen is 2 years younger than penny.
how old is jane when the total of their ages is 70.
thanks
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = Penny's age
Let +j+ = Jane's age
Let +o+ = Owen's age
Let +c+ = Carl's age
----------------------
(1) +j+=+2c+
(2) +j+=+4p+
(3) +o+=+p+-2+
(4) +j+%2B+c+%2B+p+%2B+o+=+70+
------------------------
There are 4 equations and 4 unknowns,
so it is solvable.
---------------
(1) +c+=+j%2F2+
(2) +p+=+j%2F4+
and
(3) +o+=+p+-+2+
(3) +o+=+j%2F4+-+2+
-----------------
Plug these results into (4)
(4) +j+%2B+c+%2B+p+%2B+o+=+70+
(4) +j+%2B+j%2F2+%2B+j%2F4+%2Bj%2F4+-+2+=+70+
(4) +j+%2B+j%2F2+%2B+j%2F2+=+72+
(4) +2j+=+72+
(4) +j+=+36+
and
(1) +c+=+j%2F2+
(1) +c+=+36%2F2+
(1) +c+=+18+
and
(2) +p+=+j%2F4+
(2) +p+=+36%2F4+
(2) +p+=+9+
and
(3) +o+=+j%2F4+-+2+
(3) +o+=9+-+2+
(3) +o+=+7+
-------------------
Penny's age = 9
Jane's age = 36
Owen's age = 7
Carl's age = 18
--------------
check:
(4) +j+%2B+c+%2B+p+%2B+o+=+70+
(4) +36+%2B+18+%2B+9+%2B+7+=+70+
(4) +70+=+70+
OK