Amount x Cost = Value

Question

Admission to a baseball game is $2.50 for general admission and $4.00 for reserved seats. The receipts were $3362.00 for 1187 paid admissions. How many of each ticket were sold?

Answer 1

1.) Set up 2 simultaneous equations(system of equations).

 

x+y=1187

2.5x+4y=3362.00

 

2.) Multiply each equation by a constant in order to use elimination. (notice I multiply the bottom equation by a negative factor in order to eliminate a variable

 

8 * (x+y=1187)       =      >   8x + 8y = 9496

-2 * (2.5x+4y=3362.00) = >  -5x - 8y = -6724

 

3.) Now that we have set up our two new equations we will subtract them.

 

8x + 8y = 9496

-5x - 8y = -6724

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

3x + 0y = 2772  so we get 3x = 2772. We divide by 3 and get 924.

 

so x = 924 and now we reinsert x into our first equation.

 

4.) x+y=1187 with x = 924 

 

1187 = 924 + y  subtracting 924 from each side gets us y = 263

 

Multiplying each ticket cost by its amount gets us our total of $3362.00

924*2.5 = 2310 

263*4 = 1052

= $3362.00

 

Hope this helps you solve future problems.