SOLUTION: Bill has 5 times as many baseball cards as Fred. Tim has 3 fewer than 4 times as many baseball cards as Fred. In all they have 167 baseball cards. How many does each ha

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Bill has 5 times as many baseball cards as Fred. Tim has 3 fewer than 4 times as many baseball cards as Fred. In all they have 167 baseball cards. How many does each ha      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 644761: Bill has 5 times as many baseball cards as Fred. Tim has 3 fewer than 4 times as many baseball cards as Fred. In all they have 167 baseball cards. How many does each have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +b+=+5f+
(2) +t+=+4f+-+3+
(3) +b+%2B+t+%2B+f+=+167+
There are 3 equations and 3 unknowns, so it's solvable
Substitute (2) into (3)
(3) +b+%2B+4f+-+3+%2B+f+=+167+
(3) +b+%2B+5f+=+170+
Substitute (1) into (3)
(3) +5f+%2B+5f+=+170+
(3) +10f+=+170+
(3) +f+=+17+
and, since
(1) +b+=+5f+
(1) +b+=+5%2A17+
(1) +b+=+85+
and
(2) +t+=+4f+-+3+
(2) +t+=+4%2A17+-+3+
(2) +t+=+68+-+3+
(2) +t+=+65+
Bill has 85 cards
Fred has 17 cards
Tim has 65 cards
---------------
check:
+85+%2B+17+%2B+65+=+167+
+167+=+167+
OK