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For his parents' anniversary party, Alvin is considering using one of two venues. A hotel in Lancaster will cost $80\$80 for a reservation, plus $10\$10 per person. A restaurant in the same city will cost $25\$25 per person, in addition to $50\$50 for the reservation. In order to make the best decision, Alvin figures out how many attendees it would take to have the venues cost the same amount. What would the total cost be?\newlineWrite a system of equations, graph them, and type the solution.\newline____\_\_\_\_ dollars\newline

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Mean, variance, and standard deviation of binomial distributionsright chevron icon

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Q. For his parents' anniversary party, Alvin is considering using one of two venues. A hotel in Lancaster will cost $80\$80 for a reservation, plus $10\$10 per person. A restaurant in the same city will cost $25\$25 per person, in addition to $50\$50 for the reservation. In order to make the best decision, Alvin figures out how many attendees it would take to have the venues cost the same amount. What would the total cost be?\newlineWrite a system of equations, graph them, and type the solution.\newline____\_\_\_\_ dollars\newline
  1. Set Up Equations: Let's set up the equations for both venues. For the hotel, the cost equation is C=80+10p C = 80 + 10p where p p is the number of people. For the restaurant, the equation is C=50+25p C = 50 + 25p .
  2. Find Equal Costs: To find when the costs are the same, we set the equations equal to each other: 80+10p=50+25p 80 + 10p = 50 + 25p .
  3. Solve for p: Now, solve for p p . Subtract 10p 10p from both sides to get 80=50+15p 80 = 50 + 15p . Then subtract 5050 from both sides: 30=15p 30 = 15p .
  4. Calculate p: Divide both sides by 1515 to find p p : p=2 p = 2 .
  5. Find Total Cost: Plug p=2 p = 2 back into either original equation to find the cost. Using the hotel's equation: C=80+10(2)=100 C = 80 + 10(2) = 100 .

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