SOLUTION: Mary is twice as old as Todd. In 8 years, their ages will total 70. How old is each now?

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Question 1044736: Mary is twice as old as Todd. In 8 years, their ages will total 70. How old is each now?
Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = Mary's age now
Let +t+ = Todd's age now
-------------------------
(1) +m+=+2t+
(2) +m%2B+8+%2B+t+%2B+8+=+70+
-----------------------
(2) +m+%2B+t+%2B+16+=+70+
(2) +m+%2B+t+=+54+
--------------------
substitute (1) into (2)
(2) +2t+%2B+t+=+54+
(2) +3t+=+54+
(2) +t+=+18+
and
(1) +m+=+2t+
(1) +m+=+2%2A18+
(1) +m+=+36+
-----------------
Mary is 36
Todd is 18
------------
check:
(2) +m+%2B+t+%2B+16+=+70+
(2) +36+%2B+18+%2B+16+=+70+
(2) +36+%2B+34+=+70+
(2) +70+=+70+
OK

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let Todd's age be x
if Mary is twice as old as Todd, than Mary's age is 2x
in 8 years, Todd's age will be x%2B8 and Mary's age will be %282x%2B8%29
if their ages will total 70, than
%28x%2B8%29%2B%282x%2B8%29=70
x%2B8%2B2x%2B8=70
3x%2B16=70
3x=70-16
3x=54
x=54%2F3
x=18-> Todd's age
2x=2%2A18=36 Mary's age
check:
their age in 8 from now will be:
x%2B8=18%2B8=26-> Todd's age
2x%2B8=2%2A18%2B8=36%2B8=44 Mary's age
and their sum must be 70: 26%2B44=70 which is true