Question

Isabelle and Sara are going to Mexico beach hotel in Cancun Is offering two weekend specials. One includes a 2 night stay with 3 meals and cost $195. The other includes a 3 night stay with 5 meals and costs $300. what is the cost of a single meal? Define variable system of equationstate the solution solve the system showing all steps

Answer 1

Special weekend 3.

2 night stay with 3 meals and cost $195.

Special weekend 2.

3 night stay with 5 meals and costs $300.

Based on the given information, we have

`\begin{gathered} 2x+3y=195 \\ 3x+5y=300 \end{gathered}`

Let's isolate x in the first equation

`\begin{gathered} 2x+3y=195 \\ 2x=195-3y \\ x=(195)/(2)-(3y)/(2) \end{gathered}`

Then, we combine the new equation with the second one

`\begin{gathered} 3((195)/(2)-(3y)/(2))+5y=300 \\ (585)/(2)-(9y)/(2)+5y=300 \\ (-9y+10y)/(2)=300-(585)/(2) \\ (y)/(2)=(600-585)/(2) \\ (y)/(2)=(15)/(2) \\ y=15 \end{gathered}`

Now, we find x

`\begin{gathered} x=(195)/(2)-(3\cdot15)/(2) \\ x=(195)/(2)-(45)/(2) \\ x=(150)/(2) \\ x=75 \end{gathered}`

Hence, the night stay costs $75, and each meal costs $15.