Question

Sam works as a waiter in a restaurant. He earns $1,400 per month as a base salary, plus tips averaging 15% of the meals he serves. Write a linear model for the situation, and use it to find the amount earned if Sam serves meals worth a total of $6,000.

Answer 1

Part a) The linear model is
`y=1,400+0.15x`

Part b) The amount earned is
`y=\$2,300`

Explanation:

Let

x ----> total meals worth served by Sam in a month

y ----> total earned by Sam in a month

we know that

The total earned by Sam in a month is equal to the base salary plus the total meals worth served by Sam in a month multiplied by the tips averaging in decimal form

Tips average =15%=15/100=0.15

so

`y=1,400+0.15x`

This is a linear equation in slope intercept form

`y=mx+b`

where

m is the slope or the unit rate

b is the y-intercept or initial value

The slope of unit rate is equal to

`m=0.15`

The y-intercept or b is equal to

`b=1,400`

For x=6,000

substitute in the linear equation

`y=1,400+0.15(6,000)`

`y=\$2,300`