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

$\begin{gathered} 2x+3y=195 \\ 2x=195-3y \\ x=\frac{195}{2}-\frac{3y}{2} \end{gathered}$

Then, we combine the new equation with the second one

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

Now, we find x

$\begin{gathered} x=\frac{195}{2}-\frac{3\cdot15}{2} \\ x=\frac{195}{2}-\frac{45}{2} \\ x=\frac{150}{2} \\ x=75 \end{gathered}$

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