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12. The Ryans are researching venues for their family reunion. The Picnic Place charges $150 toreserve a picnic shelter and $20 per hour to use the shelter. Totally Tents charges $300 for therental and setup of a tent and $10 per hour to use their land. How much will each company chargefor a 5-hour reunion?+At how many hours will you need to reserve the shelters for both choices to cost the same?

Respuesta :

Answer:

5-hour reunion at Picnic Place will cost $250.

5-hour reunion at Total Tent will cost $350.

15 hours for both choices to cost the same.

Explanation:

Let x represent the number of hours.

Let y represent the total cost.

For Picnic Place, our equation can be written as;

[tex]y=20x+150[/tex]

For a 5-hour reunion at Picnic Place, the charge will be;

[tex]\begin{gathered} y=20(5)+150 \\ =100+150 \\ =250 \end{gathered}[/tex]

For Total Tent, our equation can be written as;

[tex]y=10x+300[/tex]

For a 5-hour reunion, the cost will be;

[tex]\begin{gathered} y=10(5)+300 \\ y=50+300 \\ y=350 \end{gathered}[/tex]

To determine how many hours onwill need to reserve both shelters for both choices to cost the same, we just need to equate both equations and solve for x;

[tex]\begin{gathered} 20x+150=10x+300 \\ 20x-10x=300-150 \\ 10x=150 \\ x=\frac{150}{10}=15\text{hours} \end{gathered}[/tex]