Question

Mary went to the Burger Palace and bought 3 burger meals and 2 chicken meals for $43.90. Tommy bought 4burger meals and 5 chicken meals for $76.15. How much more is a burger meal than a chicken meal?

Answer 1

Okay, here we have this:

Considering the provided information, we are going to calculate how much more is a burger meal than a chicken meal, so we obtain the following:

Then from the given information we obtain the following system of equations, where x represents the price of hamburgers and the price of chicken dishes:

`\begin{gathered} 3x+2y=43.9 \\ 4x+5y=76.15 \end{gathered}`

So we'll isolate x in the first equation and replace it with it in the second:

`\begin{gathered} 3x=43.9-2y \\ x=((43.9-2y))/(3) \end{gathered}`

Replacing:

`\begin{gathered} 4((43.9-2y)/(3))+5y=76.15 \\ (175.6)/(3)-(8y)/(3)+5y=76.15 \\ (7y)/(3)=76.15-(175.6)/(3) \\ 7y=228.45-175.6 \\ y=52.85/7 \\ y=7.55 \end{gathered}`
`\begin{gathered} 3x+2y=43.9 \\ 3x+2(7.55)=43.9 \\ 3x+15.1=43.9 \\ 3x=43.9-15.1 \\ 3x=28.8 \\ x=9.6 \end{gathered}`

Finally we obtain that a hamburger is: $9.6-$7.55=$2.05 more expensive than a chicken meal.