Question

Admission to a baseball game is $3.00 for general admission and $5.50 for reserved seats. The receipts were $3277.50 for 845 paid admissions. How many of each ticket were sold?

Answer 1

Answer:

548, 297

Step-by-step explanation:

We can set this up as a system of equations. The first equation is for how many tickets were sold, which is x+y=845. The second equation is for the cost of the tickets, which is 3x+5.5y=3277.50. The best method for this problem (other than graphing) is elimination. First, we need to multiply one equation to get the opposite of one of the variables. The easiest one to do for this problem is x. The opposite of 3 is -3, so we have to multiply ALL of the first equation by -3. If you do this, then you get -3x-3y=-2535. Now, combine the equations:

3x + 5.5y = 3277.50

-3x  -3y    = -2535

________________

0x+2.5y=742.5

Now, isolate y by dividing both sides by 2.5. If you do this, you get y=297. Now, plug this in for the y in the first equation. Isolate x.

x+297=845

  -297  -297

__________

      0      548

x=548

Hope this helps!