Question

There were 598 tickets purchased for a major league baseball game the general admission tickets cost $6.50 in the upper box tickets cost $10 the total amount of money spent was $4821.50 how many of each kind of ticket were purchased?

Answer 1

Given:

a.) There were 598 tickets purchased for a major league baseball game.

b.) The general admission tickets cost $6.50.

c.) In the upper box, tickets cost $10.

d.) The total amount of money spent was $4,821.50

For us to be able to determine how many of each kind of ticket were purchased, let's first generate equations based on the given.

Let,

x = no. of general admission tickets

y = no. of upper box tickets

a.) There were 598 tickets purchased for a major league baseball game.

$\text{ x + y = 598}$

b.) The general admission tickets cost $6.50.

c.) In the upper box, tickets cost $10.

d.) The total amount of money spent was $4,821.50

$\text{ 6.50x + 10y = 4,821.5}0$

Substitute the 1st generated equation to the 2nd one and simplify.

$\text{ x + y = 598}$$\text{ y = 598 - x}$$\text{ 6.50x + 10y = 4,821.5}0$$\text{ 6.50x + 10(598 - x) = 4,821.5}0$$\text{ 6.50x + 5980 - 10x = 4,821.5}0$$\text{ 6.50x - 10x = 4,821.5}0\text{ - 5980}$$\text{ -3.50x = }-1,158.50$$\text{ }\frac{\text{-3.50x}}{-3.50}\text{ = }\frac{-1,158.50}{-3.50}$$\text{ x = }331$

Therefore, 331 tickets of the general admission were purchased.

Let's determine the number of tickets purchased for the upper box.

$\text{ x + y = 598}$$\text{ 331 + y = 598}$$\text{y = 598 - 331}$$\text{ y }=\text{ 267}$

Therefore, 267 tickets of the upper box were purchased.

In Summary,

No. of general admission tickets sold = 331 tickets

No. of upper box tickets sold = 267 tickets