company a and company b are caterers. for functions with up to 15 guests, the charges are as follows…

company a and company b are caterers. for functions with up to 15 guests, the charges are as follows: company a charges $c for $n$ guests such that $c = 100+30n$. company b charges $c for $n$ guests such that $c = 300 + 10n$. (a) for how many guests will the catering costs of both companies be the same? (b) calculate this cost.

company a and company b are caterers. for functions with up to 15 guests, the charges are as follows: company a charges $c for $n$ guests such that $c = 100+30n$. company b charges $c for $n$ guests such that $c = 300 + 10n$. (a) for how many guests will the catering costs of both companies be the same? (b) calculate this cost.

Answer

Explanation:

Step1: Set the cost - equations equal

Set $100 + 30n=300 + 10n$.

Step2: Solve for $n$

Subtract $10n$ from both sides: $100 + 30n-10n=300 + 10n-10n$, which simplifies to $100 + 20n=300$. Then subtract 100 from both sides: $100-100 + 20n=300 - 100$, getting $20n=200$. Divide both sides by 20: $n=\frac{200}{20}=10$.

Step3: Calculate the cost

Substitute $n = 10$ into either cost - equation. Using $C = 100+30n$, we have $C=100 + 30\times10=100 + 300=400$.

Answer:

(a) 10 guests (b) $400