SOLUTION: The sum of the ages of Tessie and Ato is 54 years. If Tessie's age is subtracted from twice of Ato's age the result is 6 years. Find the age of each.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The sum of the ages of Tessie and Ato is 54 years. If Tessie's age is subtracted from twice of Ato's age the result is 6 years. Find the age of each.       Log On


   

Question 1145003: The sum of the ages of Tessie and Ato is 54 years. If Tessie's age is subtracted from twice of Ato's age the result is 6 years. Find the age of each.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Tessie's age now
Let +b+ = Ato's age now
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(1) +a+%2B+b+=+54+
(2) +2b+-+a+=+6+
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(2) +2b+=+6+%2B+a+
(2) +a+=+2b+-+6+
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Plug (2) into (1)
(1) +2b+-+6+%2B+b+=+54+
(1) +3b+-+6+=+54+
(1) +3b+=+60+
(1) +b+=+20+
and
(2) +a+=+2%2A20+-+6+
(2) +a+=+40+-+6+
(2) +a+=+34+
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Tessie is 34
Ato is 20
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check:
(2) +2b+-+a+=+6+
(2) +2%2A20+-+34+=+6+
(2) +40+-+34+=+6+
(2) +6+=+6+
OK