Question 29706
<pre><b><font size = 3>A librarian bought 10 library books for a total of $138.62; how many 
at $12.95 and how many at $15.99?

There are two ways to work it.

FIRST WAY (using one unknown)

Let x = the number bought at $12.95 and 10-x be the number bought at $15.99

Then

Total money spent for the x books at $12.95 each, [or 12.95x dollars]
             
               PLUS

Total money spent for the 10-x at $15.99 each, [or 15.99(10-x) dollars]

              EQUALS

Total money spent for all the books, [or 138.62 dollars]


 12.95x + 15.99(10-x) = 138.62

Remove the decimals by multiplying through by 100

   1295x + 1599(10-x) = 13862

Remove the parentheses using the distributive principle

1295x + 15990 - 1599x = 13862

Combine the two x-terms on the left

        -304x + 15990 = 13862

Subtract 15990 from both sides

                -304x = 13862 - 15990

                -304x = -2128

Divide both sides by -304

                    x = (-2128)/(-304)

                    x = 7

So x = 7 is the number bought at $12.95 each.

Then substitute 7 for x in 10-x to find that 10-7 or 3 books were
bought ar $15.99.

-------------------------------

SECOND WAY (using two unknowns)

Let x = the number bought at $12.95 and y be the number bought at $15.99

Then the first equation coms from:

Number of $12.95 books [or s]

              PLUS

Number of $15.99 books [or y]

             EQUALS

Total number of books [or 10]

So the first equation is 

X + y = 10

Then,

Total money spent for the x books at $12.95 each, [or 12.95x dollars]
             
               PLUS

Total money spent for the 10-x at $15.99 each, [or 15.99y dollars]

              EQUALS

Total money spent for all the books, [or 138.62 dollars]


12.95x + 15.99y = 138.62

So we have the system of two equations in two unknowns

x + y = 10
12.95x + 15.99y = 138.62

Solve that system and get x=7, y=3.
 

--------------------------------------


Play tickets were $6 per adult and $4 per child. If $960 total 
sales were for 180 tickets, how many were adult?

That's the same problem except put $6 and $4 in place of 
$12.95 and $15.99, 180 in place of 10 and $960 in place of
$138.62

 6x + 4(180-x) = 960

Solve that and get 120 adult tickets and 60 children tickets.

Edwin
AnlytcPhil@aol.com</pre>