a catering company uses different functions to estimate the itemized costs for a party. the table below…

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.\ncatering cost for wait staff gratuity\n| number of guests | wait staff tip |\n| ---- | ---- |\n| 10 | $18 |\n| 20 | $36 |\n| 30 | $54 |\n| 40 | $72 |\n| 50 | $90 |\nif the tip varies directly with the number of guests, which equation represents the relationship between the tip, t, and the number of guests, g?\no t = 1.8g\no t = \\frac{g}{18}\no g = 1.8t\no g = \\frac{t}{18}

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.\ncatering cost for wait staff gratuity\n| number of guests | wait staff tip |\n| ---- | ---- |\n| 10 | $18 |\n| 20 | $36 |\n| 30 | $54 |\n| 40 | $72 |\n| 50 | $90 |\nif the tip varies directly with the number of guests, which equation represents the relationship between the tip, t, and the number of guests, g?\no t = 1.8g\no t = \\frac{g}{18}\no g = 1.8t\no g = \\frac{t}{18}

Answer

Explanation:

Step1: Recall direct - variation formula

The formula for direct variation is $t = kg$, where $t$ is the tip, $g$ is the number of guests, and $k$ is the constant of variation.

Step2: Find the constant of variation $k$

We can use any pair of values from the table. Let's take the first pair: when $g = 10$ and $t=18$. Substitute into $t = kg$ to get $18=k\times10$. Solving for $k$, we have $k=\frac{18}{10}=1.8$.

Step3: Write the equation

The equation representing the relationship between $t$ and $g$ is $t = 1.8g$.

Answer:

$t = 1.8g$