Question

at the movie theater all snacks are the same price and all movies are the same price. For snacks and tree movies cost $40. Two snacks and tree movie tickets are $32. What is the cost of a snack and movie ticket?

Answer 1

Look at the explanation.

Explanation:

The two equations:

`4s+3m=40\\2s+3m =32`

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m = The amount for each movie ticket

s = The amount for each snack

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We'll use the elimination method.

Firstly, we have to cancel either s or m. Therefore, to get the same values of either s or m, we have to multiply the entire equation.

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In here, we decided that s should be canceled first. Therefore, to get both values to have the same number, we should multiply them with each other. And since they're both positive, we have to multiply one equation with a negative number.

`(*-2)4s + 3m = 40\\(*4)2s + 3m = 32\\`

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The new equations:

`-8s -6m = -80\\8s + 12m = 128`

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Now we can cancel.

`(-8s+8s) + (-6m+12m) = (-80+128)\\\6m = 48\\m = 8`

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Solving for s:

We can choose one of the equations that we formed.

So, for instance: 8s + 12m = 128

Since we know the value of m, we can substitute it.

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`8s + 12(8) = 128\\8s + 96 = 128\\8s = 128 - 96\\8s = 32\\s = 4`

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Now we can conclude that:

1 movie ticket costs $8

1 snack costs $4