Trenton gets a job as a server in a restaurant. In addition to the $7 he gets paid for each hour he works, Trenton receives up to an additional $100 a day in tips. Write a two-variable inequality to model the given problem, where x represents the number of hours he works in a day and y represents the amount he earns. Which of the following inequalities would describe this scenario?(1 point)

Question

Responses

y≥7x+100
y greater-than-or-equal-to 7 x plus 100

y≤107x
y less-than-or-equal-to 107 x

y≤7x+100
y less-than-or-equal-to 7 x plus 100

y≤100x+7

Answer 1

To model Trenton's earnings, we need to consider both his hourly wage and the potential tips he receives.

Trenton earns $7 for each hour he works (represented by the term \(7x\)), and he can receive up to an additional $100 in tips per day. Therefore, his total earnings \(y\) can be represented by the following inequality:

\[ y \geq 7x + 0 \] (since he can earn 0 to 100 tips).

However, since he can earn tips up to $100, the correct inequality should account for the maximum possible tip amount, leading us to:

\[ y \geq 7x + 100 \]

This represents that the amount Trenton earns \(y\) is at least his hourly wage times the number of hours worked plus the tips he can receive.

So, the correct inequality that describes this scenario is:

y ≥ 7x + 100.