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.

Question

A table showing Catering Cost for Wait Staff Gratuity with two columns and 6 rows. The first column has, Number of Guests, and has the entries, 10, 20, 30, 40, 50. The second column, Wait Staff Tip, has the entries, $18, $36, $54, $72, $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 = t equals StartFraction g Over 18 EndFraction.
g = 1.8t
g = g equals StartFraction t Over 18 EndFraction.

Answer 1

To determine the equation representing the relationship between the tip \( t \) and the number of guests \( g \), we can analyze the given data:

• At 10 guests, the tip is $18: \( \frac{18}{10} = 1.8 \)
• At 20 guests, the tip is $36: \( \frac{36}{20} = 1.8 \)
• At 30 guests, the tip is $54: \( \frac{54}{30} = 1.8 \)
• At 40 guests, the tip is $72: \( \frac{72}{40} = 1.8 \)
• At 50 guests, the tip is $90: \( \frac{90}{50} = 1.8 \)

From this, we see that the tip per guest is consistently $1.80. This indicates that the total tip \( t \) varies directly with the number of guests \( g \). The relationship can be expressed as:

\[ t = 1.8g \]

Thus, the correct equation representing the relationship between the tip \( t \) and the number of guests \( g \) is:

\[ t = 1.8g \]

So the answer is \( t = 1.8g \).