Let the number of burgers be x and the number of hot dogs be y.
The question gives that the total number of items sold is 88. This can be written to be:
[tex]x+y=88\text{ -------------(1)}[/tex]The cost of a burger is $4.50 while that of hot dogs is $3.25. If the total sold price is $331, we can express this as:
[tex]4.50x+3.25y=331\text{ -----------------(2)}[/tex]This gives us a pair of equations we can solve simultaneously:
[tex]\begin{gathered} x+y=88\text{ -------------(1)} \\ 4.50x+3.25y=331\text{ -----------------(2)} \end{gathered}[/tex]To solve by substitution, make x the subject of the formula in equation (1):
[tex]x=88-y\text{ ----------(3)}[/tex]Substitute the value of x into the second equation:
[tex]\begin{gathered} 4.50(88-y)+3.25y=331 \\ 396-4.50y+3.25y=331 \\ -1.25y=331-396 \\ -1.25y=-65 \\ \therefore \\ y=\frac{-65}{-1.25} \\ y=52 \end{gathered}[/tex]To find x, we can substitute the value of y into equation (3):
[tex]\begin{gathered} x=88-52 \\ x=36 \end{gathered}[/tex]ANSWER:
The correct option is OPTION C: The food truck sold 36 burgers and 52 hot dogs.
