Answer to Question #91816 in Algebra for Tanya Ambrocio

Question

At the movie theatre, child admission is $6.00 and adult admission is $9.40 . On Saturday, 147 tickets were sold for a total sales of $1198.20. How many adult tickets were sold that day?

Answer 1

Let X represent the number of children and Y for the number of adults.

we get the equation

x + y =146

6x + 9.4y = $1198.20

Let's start by solving 6x+9.4y = 1198.2 for the variable x.

Move the 9.4y to the right hand side by subtracting 9.4y from both sides, 

6x = 1198.2-9.4y 

x = 199.7-1.56667y

Next, let's solve x+y = 147 for the variable y.

y = 147-x

Now, plug the earlier result, x=199.7-1.56667y, in for x everywhere it occurs in 

y=147-x.

This gives y=147-(199.7-1.56667y). Now all we have to do is solve this for y,to have our first solution.

Multiply y and 1.56667

Multiply y and 1

1.56667*y evaluates to 1.56667y

199.7-1.56667*y evaluates to 199.7-1.56667y

147 - 199.7 = -52.7

The answer is -52.7+1.56667y

147-(199.7-1.56667*y) evaluates to -52.7+1.56667y

Move the 1.56667y to the left hand side by subtracting 1.56667y from both sides, like this:

From the left hand side:

y - 1.56667y = -0.56667y

The answer is -0.56667y

The answer is -52.7

Now, the equation reads:

-0.56667y = -52.7 

To isolate the y, we have to divide both sides of the equation by the other variables

around the y on the left side of the equation.

The last step is to divide both sides of the equation by -0.56667 like this:

To divide y by 1

The y just gets copied along in the numerator.

The answer is y

-0.56667y ÷ -0.56667 = y

-52.7 ÷ -0.56667 = 92.9995

The solution to your equation is:

y = 92.9995

Lastly, to find the solution for x, we plug this answer for y into the earlier result that

x=199.7-1.56667y.

This gives x=199.7-1.56667(92.9995). Now, simplify this.

Multiply 1.56667 and 92.99951

1.56667*(92.9995) evaluates to 145.7

199.7-1.56667*(92.9995) evaluates to 54.0005

x= 54.0005

So, the solutions to your equations are:

x= 54.0005 and y= 92.9995

Therefore there were 93 Adults and 54 children

Answer = 93