unit 2: #9\ninformation about the costs of three catering companies is shown in this table.\n| acme catering…

unit 2: #9\ninformation about the costs of three catering companies is shown in this table.\n| acme catering company | best foods company | creative catering company |\n| --- | --- | --- |\n| $6 per person plus a flat $100 service charge | $8 per person plus a flat $40 service charge | $10 per person with no service charge |\ngavin can spend no more than $300 on the catering for an event.\nwhat is the greatest number of people that gavin can have at his event without spending more than $300 on catering?\n(a) 30\n(b) 32\n(c) 33\n(d) 37

unit 2: #9\ninformation about the costs of three catering companies is shown in this table.\n| acme catering company | best foods company | creative catering company |\n| --- | --- | --- |\n| $6 per person plus a flat $100 service charge | $8 per person plus a flat $40 service charge | $10 per person with no service charge |\ngavin can spend no more than $300 on the catering for an event.\nwhat is the greatest number of people that gavin can have at his event without spending more than $300 on catering?\n(a) 30\n(b) 32\n(c) 33\n(d) 37

Answer

Explanation:

Step1: Set up cost - equations for each company

Let $x$ be the number of people. For Acme Catering Company, the cost $C_{A}=6x + 100$. For Best Foods Company, the cost $C_{B}=8x+40$. For Creative Catering Company, the cost $C_{C}=10x$.

Step2: Solve for $x$ in each cost - equation with $C\leq300$

For Acme Catering Company: Set $C_{A}=6x + 100\leq300$. Subtract 100 from both sides: $6x\leq300 - 100=200$. Then $x\leq\frac{200}{6}\approx33.33$. For Best Foods Company: Set $C_{B}=8x + 40\leq300$. Subtract 40 from both sides: $8x\leq300 - 40 = 260$. Then $x\leq\frac{260}{8}=32.5$. For Creative Catering Company: Set $C_{C}=10x\leq300$. Divide both sides by 10: $x\leq30$.

Step3: Compare the maximum number of people for each company

We have $x_{A}\approx33.33$, $x_{B}=32.5$, $x_{C}=30$. Since the number of people $x$ must be an integer, the greatest value of $x$ among these non - exceeding values is 32.

Answer:

B. 32