Question

1. ellie earns $12.50 per hour as a server working x hours per week. she also earns $9.50 per hour editing poetry for y hours per week. ellie needs to make at least $145 to pay her cell phone bill, but she has at most 23 total hours per week with her busy college schedule. the system of linear inequalities modeling this situation is shown.

12.50x + 9.50y ≥ 145
x + y ≤ 23
which statement(s) represents a solution to the system of linear inequalities?
a. ellie can work as a server for 4 hours and edit poetry for 10 hours.
b. ellie can work as a server for 13 hours and edit poetry for 10 hours.
c. ellie can work as a server for 4 hours and edit poetry for 19 hours.
d. ellie can work as a server for 10 hours and edit poetry for 19 hours.

Explanation:

Step1: Check option A

For $x = 4$ and $y = 10$:
First inequality: $12.50\times4+9.50\times10=50 + 95=145$, and $145\geq145$.
Second inequality: $4 + 10=14\leq23$.

Step2: Check option B

For $x = 13$ and $y = 10$:
First inequality: $12.50\times13+9.50\times10=162.5+95 = 257.5\geq145$.
Second inequality: $13 + 10=23\leq23$.

Step3: Check option C

For $x = 4$ and $y = 19$:
First inequality: $12.50\times4+9.50\times19=50+180.5 = 230.5\geq145$.
Second inequality: $4+19 = 23\leq23$.

Step4: Check option D

For $x = 10$ and $y = 19$:
Second - inequality: $10 + 19=29>23$, so it does not satisfy $x + y\leq23$.

Answer:

A. Ellie can work as a server for 4 hours and edit poetry for 10 hours.
B. Ellie can work as a server for 13 hours and edit poetry for 10 hours.
C. Ellie can work as a server for 4 hours and edit poetry for 19 hours.