The concession stand is selling hot dogs and hamburgers during a game. At halftime, they sold a total of 78 hot dogs and hamburgers and brought in $105.50. how many of each item did they sell if hamburgers sold for $1.50 and hot dogs sold for $1.25?
The concession stand sold
The first thing to do in algebraic problems is assign variables to things we don't know, so let's start there:
- We don't know how many hot dogs the concession stand sold, so we will call that number
- We don't know how many hamburgers the concession stand sold, so we will call that number
Now we translate the statements into algebraic equations:
- The number of hot dogs and hamburgers that were sold is
#78#, so #d+h=78#.
- If each hot dog is sold for
#1.25#, then the total revenue from hot dogs is given by #1.25d#. In the same way, the total revenue from hamburgers is #1.50h#. The total revenue from both hot dogs and hamburgers should be the sum of these, and since we are told the total revenue is #105.50#, we can say #1.25d+1.5h=105.5#.
We now have a system of two linear equations:
We can solve it using several methods, though I'm going to go with substitution. Use the first equation to solve for
Now plug this in for
The concession stand therefore sold