Respuesta :
We know that
• Four cheeseburgers and five small fries have a total of 2,310 calories.
,• Three cheeseburgers and two small fries have a total of 1,330 calories.
Let's call c cheeseburgers and f small fries.
Based on the given information, we can define the following system.
[tex]\begin{gathered} 4c+5f=2,310 \\ 3c+2f=1,330 \end{gathered}[/tex]To solve this system, we multiple the first equation by -3/4 to eliminate c and find the value for f
[tex]\begin{gathered} -3c-\frac{15}{4}f=-\frac{6,930}{4} \\ 3c+2f=1,330 \end{gathered}[/tex]Now, we sum the equations to get one equation with f
[tex]\begin{gathered} \frac{8f-15f}{4}=\frac{5,320-6,930}{4} \\ -7f=-1,610 \\ f=\frac{-1,610}{-7} \\ f=230 \end{gathered}[/tex]This means one small fries has 230 calories.
We use this value to find the calories for a cheeseburger.
[tex]\begin{gathered} 3c+2(230)=1,330 \\ 3c+460=1,330 \\ 3c=1,330-460 \\ 3c=870 \\ c=\frac{870}{3} \\ c=290 \end{gathered}[/tex]