SOLUTION: Kate's age exceeds twice Martha's age by 6 years. Eight years ago, four times Martha's age exceeded Kate's age by 6 years. Find their present ages.
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Question 130466: Kate's age exceeds twice Martha's age by 6 years. Eight years ago, four times Martha's age exceeded Kate's age by 6 years. Find their present ages. Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! Let x=Martha's present age; x-8=Martha's age 8 years ago
Then 2x+6=Kates present age; (2x+6)-8=2x-2=Kates age 8 years ago
Now we are told that:
4(x-8)=2x-2+6 get rid of parens
4x-32=2x+4 subtract 2x from each side and add 32 to each side
4x-2x-32+32=2x-2x+4+32 collect like terms
2x=36 divide both sides by 2
x=18-----------------Martha's present age
2x+6=2*18+6=42-------------------Kates present age
CK
---Kate's age exceeds twice Martha's age by 6 years---
2*18+6=42
42=42
also
----Eight years ago, four times Martha's age exceeded Kate's age by 6 years---
4*(18-8)=(42-8)+6
4*10=44+6
40=40
