Question

There were 436 tickets purchased for a major league baseball game. The general admission tickets cost ​$6.50 and the upper reserved tickets cost ​$8.00. The total amount of money spent was ​$3284.00. How many of each kind of ticket were​ purchased?
How many general admission tickets were​ purchased? ____
How many upper reserved tickets we purchased? ___

Answer 1

Answer:

How many general admission tickets were​ purchased? __136__

How many upper reserved tickets we purchased? _300_

Step-by-step explanation:

Let the number of general tickets = g.

Let the number of reserved tickets = r.

6.5g + 8r = 3284

g + r = 436

     6.5g + 8r = 3284

(+)   -8g + -8r = -3488

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

     -1.5g         = -204

g = 136

g + r = 436

136 + r = 436

r = 300

Answer:

How many general admission tickets were​ purchased? __136__

How many upper reserved tickets we purchased? _300_

Answer 2

Answer:

136 general admission tickets were purchased

300 upper reserved tickets were purchased

Step-by-step explanation:

This is a classic system of equations problem. Let the number of general admission tickets sold be $g$ and the number of reserved tickets sold be $r$. We can write the following system of equations:

$\begin{cases}6.50g+8.00r=3284,\\g+r=436\end{cases}$

Multiply the second equation by -8 and add both equations to isolate $g$:

$-8(g+r)=-8(436),\\-8g-8r=-3488,\\\begin{cases}6.50g+8.00r=3284,\\-8g-8r=-3488\end{cases},\\-1.5g=-204,\\g=\frac{-204}{-1.5}=\boxed{136}$

Now substitute $g=136$ into $g+r=436$ to find the number of reserved tickets sold:

$g+r=436,\\136+r=436,\\r=436-136=\boxed{300}$