item 4: information about the costs of three catering companies is shown in this table. catering company…

item 4: information about the costs of three catering companies is shown in this table. catering company costs acme catering company best foods company creative catering company $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 gavin can spend no more than $300 on the catering for an event. what is the greatest number of people that gavin can have at his event without spending more than $300 on catering? a 30 b 32 c 33 d 37

item 4: information about the costs of three catering companies is shown in this table. catering company costs acme catering company best foods company creative catering company $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 gavin can spend no more than $300 on the catering for an event. what is the greatest number of people that gavin can have at his event without spending more than $300 on catering? a 30 b 32 c 33 d 37

Answer

Explanation:

Step1: Set up 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 $6x + 100\leq300$. Subtract 100 from both sides: $6x\leq300 - 100=200$. Then $x\leq\frac{200}{6}=\frac{100}{3}\approx33.33$.

For Best Foods Company:

Set $8x + 40\leq300$. Subtract 40 from both sides: $8x\leq300 - 40 = 260$. Then $x\leq\frac{260}{8}=32.5$.

For Creative Catering Company:

Set $10x\leq300$. Divide both sides by 10: $x\leq30$.

Step3: Compare the maximum values of $x$ for each company

The maximum number of people for Acme is approximately 33, for Best Foods is 32, and for Creative is 30.

Answer:

b. 32