Let x be the number of hours stacey worked on Saturday.
For hte first 4 hours, she earned $100 and $20 every additional hour.
Since her total hours is x, we will subtract 4 from it and that will be the number of hours she worked for $20
[tex]100+20(x-4)[/tex]She earned at most $160, equating the expression above less than or equal to 160.
[tex]\begin{gathered} 100+20(x-4)\le160 \\ 20(x-4)\le160-100 \\ 20x-80\le60 \\ 20x\le60+80 \\ 20x\le140 \\ x\le\frac{140}{20} \\ x\le7 \end{gathered}[/tex]Her total number of hours will be x ≤ 7
Since Stacey needs to work at most 7 hours to get $160
The number of hours she will need is 7 hours
Let's check.
Subsitute x = 7 to the expression above :
[tex]\begin{gathered} 100+20(x-4) \\ \Rightarrow100+20(7-4) \\ \Rightarrow100+20(3) \\ \Rightarrow100+60 \\ \Rightarrow160 \end{gathered}[/tex]Therefore, the answer is correct.
