SOLUTION: Lee's mother's age is two times more than three times Lee's age. the sum of their ages is 54. Could you please determine their ages and when Lee's age be half his mother's age.

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Lee's mother's age is two times more than three times Lee's age. the sum of their ages is 54. Could you please determine their ages and when Lee's age be half his mother's age.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1156680: Lee's mother's age is two times more than three times Lee's age. the sum of their ages is 54.
Could you please determine their ages and when Lee's age be half his mother's age.
Thank you!

Found 2 solutions by VFBundy, josmiceli:
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Lee's age = x
Lee's mother's age = 3x + 2

x + (3x + 2) = 54
4x + 2 = 54
4x = 52
x = 13

Lee's age = x = 13
Lee's mother's age = 3x + 2 = 39 + 2 = 41

-------------------------------------------------

When will Lee's age be half his mother's age?:

13 + n = (41 + n)/2
2(13 + n) = 41 + n
26 + 2n = 41 + n
n = 15 years

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Lee's age
Let +b+ = Lee's mother's age
-----------------------------------------
(1) +b+=+3a+%2B+2+
(2) +a+%2B+b+=+54+
-----------------------------
Plug (1) into (2)
(2) +a+%2B+3a+%2B+2+=+54+
(2) +4a+=+52+
(2) +a+=+13+
and
(1) +b+=+3a+%2B+2+
(1) +b+=+3%2A13+%2B+2+
(1) +b+=+41+
---------------------------
Note that the difference in their ages
never changes. The difference is
+41+-+13+=+28+
====================================
When Lee's age be half his mother's age:
+a+=+%28+1%2F2+%29%2Ab+
+a+=+%28+1%2F2+%29%2A%28+a+%2B+28+%29+
+2a+=+a+%2B+28+
+a+=+28+
and
+b+=+a+%2B+28+
+b+=+28+%2B+28+
+b+=+56+
----------------------
Lee will be 28
Lee's mother will be 56