SOLUTION: At Bob’s garage sale, all books were one price, and all magazines were another price. Sam bought five books and three magazines for $2.50, and William bought two books and two mag

At Bob’s garage sale, all books were one price, and all 
magazines were another price.  Sam bought five books and 
three magazines for $2.50, and William bought two books 
and two magazines for $1.70.  What was the price of a 
book and what was the price of a magazine?

I think you made a mistake and mistyped, but I'll work it 
just as it is stated.  However it turns out that the seller 
only charges for his magazines.  The seller pays people to
take away his books!
 
Let B dollars = the price of a book
Let M dollars = the price of a magazine

>>...Sam bought five books and three magazines for $2.50...<<

Then the price of 5 books = 5 times B dollars or 5B dollars 
and the price of 3 mags = 3 times M or dollars 3M dollars

      5B + 3M = 2.50

>>...William bought two books and two magazines for $1.70...<<

Then the price of 2 books = 2 times B dollars or 2B dollars 
and the price of 2 mags = 2 times M or dollars 2M dollars

      2B + 2M = 1.70

So we have this system of equations:

      5B + 3M = 2.50
      2B + 2M = 1.70

Solution: B = -.025, M = .875 

That's a negative price for a book.  That means the seller 
paid people 2 1/2 cents just to take the books away.  
However he charged 87 1/2 cents for each magazine.

Let's check:

>>...Sam bought five books and three magazines for $2.50...<<

The seller paid Sam 2 1/2 cents for every book he took away.
So Sam got paid 12 1/2 cents for the 5 books he
took away.  But then he had to pay 87 1/2 cents apiece for the
three magazines, or $2.62 1/2, but the 12 1/2 cents he got paid
for the books, brought his cost down to $2.50.

>>...William bought two books and two magazines for $1.70...<<

The seller paid William 2 1/2 cents for every book he took away.
So William got paid 5 cents for the 2 books he took away.  But 
then he had to pay 87 1/2 cents apiece for the two magazines,
or $1.75, but the 5 cents he got paid for taking away the books,
brought his cost down to $1.70. 

It certainly checks! That's a very strange answer indeed, yet 
it is mathematically correct!  If you find you have made a 
mistake, then repost and we'll solve it too.  But it will be 
the same principle.  We just normally don't expect a word 
problem to come out with a negative cost, which means people got
paid to haul the books away!

Edwin