word problem

Question

A total of 825 tickets were sold for a game for a total of 1,462.50. If adult tickets sold for $ 2.00 and children's tickets sold for $ 1.50. how many of each kind of tickets were sold?

Answer 1

Hy Cindy,

 

Let A be the number of adult tickets sold and C be the number of children's tickets sold.

 

Now let's form a system of equations.

 

A + C = 825

2A + 1.50C = 1462.50

 

You can now use either substitution or elimination and solve the above system of equation.

 

Multiply the first equation by -2 and add it to the second equation.

 

-2A - 2C = -1650

+2A + 1.5C = 1462.50

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

 

-0.5 C = -187.5

 

C = 375

 

Now substitute this value for C into the first equation.

 

A + 375 = 825

 

A = 450

 

There were 450 adult tickets and 375 child tickets sold.

 

 

You can plug these 2 values into the original 2 equations and check if they are correct.

Good luck with all of your problems.

 

 

regards,

 

mayuran

 

Answer 2

There are two variables and two equations -- that's enough to solve for both variables.

 

Let:

   x = number of adult tickets

   y = number of student tickets

 

Now, the important concept is that the money from adult tickets is (price of adult tickets)*(number of adult tickets).  The same is true for student tickets.

 

Translate:

"825 tickets were sold"     means     x+y = 825     [eq1]

 

"total of 1,462.50"    means

  adult ticket money   +   children ticket money   =    $1462.50

        $2,00x             +       $1.50y                    = $1462.50           [see above note]     [eq2]

 

You may use either (1) substitution or (2) elimination.  Let's use substitution.

   Solve eq1 for one of the variables in terms of the other:

          y = 825 - x    

   Now, substitute for y in eq2:

      $2.00x    +   $1,50(825-x)  = $1462.50

       200x     +  123750  -  150x  =  146250      [multiply by 100; cancel $]

        50x = 22500                    [collect terms; subtract 123750 from both sides]

          x = 450      [there were 450 adult tickets sold]

        y = 825 - 450 = 375 child tickets sold

 

Check:

     Is   450 + 375 = 825   ?

             825 = 825   ?yes

    Is   2.00(450) + 1.50(375) = 1462.50   ?

               1462.50 = 1462.50   ?yes