intermediate algebra

Question

700 tickets were sold for a game for a total of $1,450.00. If adult tickets sold for $2.50 and children's tickets sold for $1.50, how many of each kind of ticket were sold?

They sold  adult tickets and  children's tickets.

Answer 1

If we let the variable a represent the number of adult tickets sold and the variable s represent the number of student tickets sold, then we can write the following equation to show the total number of tickets sold:

a + s = 700 tickets

For the costs, we can write:

2.50 a + 1.50 s = 1450

If we solve the first equation for s :

s = 700 - a

Then we can substitute this representation of s into the cost equation:

2.50 a + 1.50 (700 - a) = 1450

Solve this equation for a using the distributive property and combining like terms:

2.50 a + 1050 - 1.50 a = 1450

1.00 a + 1050 = 1450

1.00 a + 1050 - 1050 = 1450 - 1050

1.00 a = 400

OR a = 400 adult tickets

Then s will be equal to 700 - a OR

700 - 400 = 300 student tickets

To verify:

$2.50 * 400 + $1.50 * 300 = $1450

$1000 + $450 = $ 1450