At a baseball game Gina purchased 6 hotdogs and 3 nachos for $24. Fred bought 8 hotdogs and 1 nacho for $23. How much is a hotdog?

1 Answer
Feb 20, 2018

Let the price of hotdogs be #h#
Let the price of nachos be #n#.

For the first sentence, Gina bought #6# hotdogs and #3# nachos, which must equal to #24#. Let's put this into an equation.
#6h + 3n = 24#
Let's simplify this by dividing both sides by #3#.
#2h + n = 8#

Fred bought #8# hotdogs and #1# nacho for #23#. Here's the equation:
#8h + n = 23#

This is now a system of equations, were we can use both equations and solve.

There are a few ways of solving this: graphing, substitution, and elimination. I'm going to use substitution.
Since we want to know the price of a hotdog, let's find #h#:

If we put #n# by itself in the first equation, it will become #n = 8 - 2h#. Now let's substitute this value in for #n# in the second equation:
#8h + (8-2h) = 23#
and simplify...
#6h + 8 = 23#
#6h = 15#
#h = 2.5#

Therefore, hotdogs are #$2.5# each.

Hope this helps!