At the hot dog stand, it costs 18.39 for five hotdogs and six bags of chips. If it costs 4.63 for one hot dog and two bags of chips, how much is a hotdog?

Let's say that one hotdog = x and one bag of chips = y

5 hotdogs + 6 bag of chips = $ 18.39 or 5x + 6y = $18.39

1 hotdog + 2 bag of chips = $4.63 or x + 2y = $4.63

We can then take the second equation and set it equal to x by subtracting 2y from both sides so that

x = $4.63 - 2y

Now that we know what x is equal to, we can substitute [$4.63 - 2y] into the first equation

Like so: 5[$4.63 - 2y] + 6y = $18.39

Now we only have one variable, which means we can solve for y now.

First we should distribute the 5

5 ($4.63) - 5 (2y) + 6y = $18.39

$23.15 - 10y + 6y = $18.39

Then we can add like-terms (y terms)

$23.15 - 4y = $18.39

Next we can subtract $23.15 from both sides to isolate the variable

-4y = $18.39 - $23.15

-4y = - $4.76

Lastly, we can divide both sides by a - 4

-4y/-4 = - $4.76/-4

y = $1.19

This means that one bag of chips costs $1.19

Now that we know what y equals, we can plug that number into our equation for x

x = $4.63 - 2y

x = $4.63 - 2 ($1.19)

x = $4.63 - $2.38

x = $2.25

This means that one hotdog costs $2.25