At the hotdog stand it cost $18.39 for five hotdogs and six bags of chips if it cost $4.63 for one hotdog and two bags of chips how much is a hotdog

Answer 1

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

Answer 2

There is a MUCH faster solution: Multiply the 2nd equation by three, giving you 3x + 6y = $13.89 Subtract this from the first equation, yielding 2x = $4.50, so x [the hot dog] = $2.25 Feel free to call me about other shortcuts to difficult problems. Dr. Gary Dubler 561-509-8558