SOLUTION: Kenna, Lexy and Lupe went to a popular clothing store and spent a total of $500.00 Lupe spent $5.00 more than half of what Lexy spent and Kennan spent three times what Luke spent.

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Kenna, Lexy and Lupe went to a popular clothing store and spent a total of $500.00 Lupe spent $5.00 more than half of what Lexy spent and Kennan spent three times what Luke spent.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 574156: Kenna, Lexy and Lupe went to a popular clothing store and spent a total of $500.00 Lupe spent $5.00 more than half of what Lexy spent and Kennan spent three times what Luke spent.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +k+ = amount Kenna spent
Let +x+ = amount Lexy spent
Let +p+ = amount Lupe spent
given:
(1) +k+%2B+x+%2B+p+=+500+
(2) +p+=+%281%2F2%29%2Ax+%2B+5+
(3) +k+=+3p+
------------
This is 3 equations and 3 unknowns
so it should be solvable
------------
(2) +%281%2F2%29%2Ax+=+p+-+5+
(2) +x+=+2p+-+10+
Substitute (2) and (3) into (1)
(1) +3p+%2B+2p+-+10+%2B+p+=+500+
(1) +6p+=+500+%2B+10+
(1) +6p+=+510+
(1) +p+=+85+
and, since
(3) +k+=+3p+
(3) +k+=+3%2A85+
(3) +k+=+255+
and
(2) +x+=+2p+-+10+
(2) +x+=+2%2A85+-+10+
(2) +x+=+170+-+10+
(2) +x+=+160+
$255 is the amount Kenna spent
$160 is the amount Lexy spent
$85 is the amount Lupe spent
check:
(1) +k+%2B+x+%2B+p+=+500+
(1) +255+%2B+160+%2B+85+=+500+
(2) +500+=+500+
OK