Respuesta :
Let p = # of people she can invite.
[tex] 6.50p+100\leq500 [/tex]
Let's break down what this inequality is saying. Since there is a $100 setup fee, we can add 100 dollars to the inequality. The 6.50p represents the fee per person. So, when we solve for p, this will give us the maximum people she can invite. The cost cannot go above 500 dollars, but it can be less than or equal to. Let's solve:
[tex] 6.50p+100\leq500 [/tex]
[tex] 6.50p\leq400 [/tex]
[tex] p=61.54 [/tex]
However, since you can't invite 61 and a half people, you will have to round the answer down to the nearest whole number, which would be 61.
Anna can invite 61 people maximum while staying within her budget.
Anna can invite 61 persons in her budget.
Total Cost
We know that for any event involving fixed cost and variable cost the equation is given as,
[tex]\bold{Total\ budget=Fixed cost+(Variable\ cost\times Number\ of\ Units)}[/tex]
Given to us,
setup charge = $100,
charge per person = $6.50,
Total budget = $500,
Anna Budget
As we know that the setup cost is the fixed cost and plate charge per person is the variable cost for this case. therefore,
[tex]\bold{Total\ budget=Fixed cost+(Variable\ cost\times Number\ of\ Units)}[/tex]
[tex]\bold{Total\ budget=Setup\ cost+(Charge\ per\ person\times Number\ of\ person)}[/tex]
Substituting values we get,
[tex]\bold{\$500=\$100+(\$6.50\times Number\ of\ person)}[/tex]
[tex]\bold{\$500-\$100=(\$6.50\times Number\ of\ person)}[/tex]
[tex]\bold{\$400=(\$6.50\times Number\ of\ person)}[/tex]
[tex]\bold{\dfrac{\$400}{\$6.50}=Number\ of\ person}[/tex]
[tex]\bold{Number\ of\ person=61.538 \approx 61 persons}[/tex]
Hence, Anna can invite 61 persons in her budget.
Learn more about Total Cost:
https://brainly.com/question/15853856
