Question

initial discussion prompt
read the scenario below and answer any questions.

1. you are planning a party on a limited budget. in order to do so you will need to determine how much it will cost (total) to rent a space and pay per person for meals. if the cost of the rental space is $780 and the price per person for food is $9.75, how much would it cost to host 50 people for the party? in your post, please write a linear equation in the form of y = mx + b to model the scenario. give a description of what each letter stands for that makes sense for this situation. then, substitute the numbers in and solve to show the total cost for 50 people.
2. if your budget was $1500 total, how many people can you invite? write a similar equation and solve to find out how many guests you could invite with a total budget of $1500.

post two peer responses to classmates posts
dont worry if you are wrong! once you post, you can see what others did and others can help you. did you like/understand their explanation? if its different than yours, can you suggest how they can fix it or how you can fix yours?

Explanation:

Step1: Write the linear equation

Let \(y\) be the total cost, \(x\) be the number of people. The fixed cost \(b = 780\) (rental space cost) and the variable cost per person \(m=9.75\) (food cost per person). The linear equation is \(y = 9.75x+780\).

Step2: Find the cost for 50 people

Substitute \(x = 50\) into the equation \(y=9.75x + 780\).

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Step3: Solve for the number of people with a budget of \(y = 1500\)

Substitute \(y = 1500\) into the equation \(1500=9.75x + 780\).
First, subtract 780 from both sides: \(1500 - 780=9.75x\), so \(720 = 9.75x\).
Then divide both sides by 9.75: \(x=\frac{720}{9.75}=\frac{720\times4}{9.75\times4}=\frac{2880}{39}\approx73.85\). Since we can't invite a fraction of a person, \(x = 73\).

Answer:

1. The linear equation is \(y = 9.75x+780\) (where \(y\) is total cost, \(x\) is number of people). The cost for 50 people is \(\$1267.5\).
2. With a budget of \(\$1500\), you can invite 73 people.