please help with this math equation

Question

At the movie theatre, child admission is $6.00

 and adult admission is $9.30

. On Saturday, 165

 tickets were sold for a total sales of $1293.60

. How many adult tickets were sold that day?

Answer 1

Hello,

Let's set x equal to the number of child tickets sold and y equal to the number of adult tickets sold.

This give us two equations:

x + y = 165 (this comes from the problem telling us that 165 tickets total were sold on Saturday)

6x + 9.3y = 1293.60 (child tickets cost $6 and adult tickets cost $9.30)

Taking the first equation, we can solve x.

x + y = 165

x = 165 - y (move the y to the other side by subtracting y)

Now, we'll plug x, which we just solved for, into the second equation.

So, 6x + 9.3y = 1293.60 turns into:

6(165 - y) + 9.3y = 1293.60

Multiply the 6 through to get:

990 - 6y + 9.3y = 1293.60

Combine the y's and move 990 to the other side via subtractuion:

3.3y = 303.60

Divide each side by 3.3

y = 92 adult tickets

Having solved for y, we know that 92 adult tickets were sold that day. If the question wanted to know how many child tickets, we simply plug y = 92 into the first equation:

x + y = 165

x + 92 = 165

x = 73 child tickets

Check your work:

73*$6 + 92*$9.3 = $1293.60

Let me know if I can provide more clarity!