Question

lorenzo wants to know how much it will cost to rent tables and chairs for an event. he investigates renting tables and chairs and decides to use two different companies.
company a
$4 per table (seats 4) and a $25 one - time delivery and pickup fee
company b
$2 per chair and a $15 one - time delivery and pickup fee
each table seats 4 people, so lorenzo needs to rent 4 chairs for every table.
x = number of tables
cost to rent tables from company a: $f(x)=4x + 25$
cost to rent chairs from company b: $g(x)=2(4x)+15$
which function represents the total cost for lorenzo to rent $x$ number of tables and the chairs he needs to go with them?
\bigcirc $12x$

Explanation:

Step1: Define total cost function

Total cost \( C(x) \) is the sum of cost from Company A (\( f(x) \)) and cost from Company B (\( g(x) \)). So \( C(x)=f(x)+g(x) \).

Step2: Substitute \( f(x) \) and \( g(x) \)

Given \( f(x) = 4x + 25 \) and \( g(x)=2(4x)+15 = 8x + 15 \). Substitute into \( C(x) \):
\( C(x)=(4x + 25)+(8x + 15) \)

Step3: Combine like terms

Combine \( x \)-terms and constant terms: \( 4x+8x=12x \), \( 25 + 15 = 40 \). So \( C(x)=12x + 40 \). But since the option given is \( 12x \) (maybe a partial or mis - presented option, but following the calculation of the linear term), the linear term of the total cost function's variable part is \( 12x \).

Answer:

\( 12x \) (Note: The full total cost function should be \( 12x + 40 \), but based on the given option and the calculation of the \( x \)-term, the answer is \( 12x \))