SOLUTION: you have used all of a $50 gift certificate watching movies at the local theater. Afternoon movies are $4 and evening movies are $6. you have watched a total of 10 movies. HOw much

Question 153240: you have used all of a $50 gift certificate watching movies at the local theater. Afternoon movies are $4 and evening movies are $6. you have watched a total of 10 movies. HOw much have you spent on evening movies?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=# of $6 movies and y=# of $4 movies

Since "you have watched a total of 10 movies", this means that the first equation is

Also, since you only have $50 to spend, this means that the second equation is

So we have the system of equations:

Let's use substitution to solve this system.

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

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

Since , we can now replace each in the second equation with to solve for

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Combine like terms on the left side

Subtract 40 from both sides

Combine like terms on the right side

Divide both sides by 2 to isolate x

Divide

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and

This means that you bought 5 $6 movies and 5 $4 movies

RELATED QUESTIONS
You have a gift certificate for $40 to use at a movie theater. Matinees cost $5 and... (answered by Alan3354)

Lesley has a gift card worth $500 for a local entertainment store. Movies cost $20 each... (answered by MathLover1)

You join a movie club that allows you to stream movies at a reduce rate. Your bill last... (answered by JulietG)

In a special movie club, you have a choice of watching any 3 movies out of 45... (answered by addingup)

hello, We have a story problem, and have to solve it with a linear equation, either... (answered by josgarithmetic)

Molly receives a $25 dollar gift card to her favorite movie theater. It costs $6.50 for... (answered by macston)

While attending a film festival you decide that there are 13 movies that you are... (answered by ewatrrr)

Owen spent 1/3 of his monthly pay check at the movies. He also received a $25 gift... (answered by rfer)

Suppose you are conducting an experiment to determine the preferences of Netflix users... (answered by ikleyn)