Question

a catering company uses different functions to estimate the itemized costs for a party. the table below represents the included tip for wait staff as a function of the number of guests served.
catering cost for wait staff gratuity

number of guests	wait staff tip
20	$36
30	$54
40	$72
50	$90

if the tip varies directly with the number of guests, which equation represents the relationship between the tip, t, and the number of guests, g?
○ $t = 1.8g$
○ $t = \frac{g}{18}$
○ $g = 1.8t$
○ $g = \frac{1}{18}$

Explanation:

Step1: Recall direct variation formula

Direct variation is \( t = kg \), where \( k \) is the constant of proportionality.

Step2: Calculate \( k \) using a data point

Take \( g = 10 \), \( t = 18 \). Substitute into \( t = kg \):
\( 18 = k \times 10 \)
Solve for \( k \): \( k=\frac{18}{10}=1.8 \)

Step3: Form the equation

Substitute \( k = 1.8 \) into \( t = kg \): \( t = 1.8g \)

Answer:

\( t = 1.8g \) (the first option)