Question

Samantha works as a waitress in a restaurant. She earns $800 per month as a base salary, plus tips averaging 15% of the meals she serves. Write a linear model for the situation. Then use it to find the amount earned if Samantha serves meals worth a total of $1000.

Answer 1

a) linear model is
`y= 800+(0.15)x`

b) Amount earned by Samantha is $950.

Explanation:

Given: Samantha base salary= $800

She get tips averaging 15% of the meals she serves.

Samantha serve meals worth a total of $1000.

Lets assume total worth of meal served by Samantha be "x".

And Total earning of samantha in a months be "y".

To calculate the total income of samantha, we need to add fixed income and variable income.

∴
`y= fixed\ salary+ Tips\ on\ meals\ served`

`y= 800+ ((15)/(100)) * x` (∵ Tip is 15%)

∴
`y= 800+(0.15)x`

Hence, the linear model for the total earning of samantha is
`y= 800+(0.15)x`.

Now, finding the total amount earned by samantha.

As given, Samantha serves meals worth a total of $1000.

Subtituting the value of meals worth in the equation.

`y= \$ 800+ (0.15)* \$ 1000`

⇒
`y= \$ 800+\$ 150`

∴ y= $950

Hence, the total amount earned by Samantha is $950.