Question

Stacey earned $100 for 4 hour plus 20 every additional hour babysitting on Saturday.She earned at most $160 in all.a)Write an inequality that represents how much Stacey worked on Saturday.

Answer 1

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

`100+20(x-4)`

She earned at most $160, equating the expression above less than or equal to 160.

`\begin{gathered} 100+20(x-4)\le160 \\ 20(x-4)\le160-100 \\ 20x-80\le60 \\ 20x\le60+80 \\ 20x\le140 \\ x\le(140)/(20) \\ x\le7 \end{gathered}`

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 :

`\begin{gathered} 100+20(x-4) \\ \Rightarrow100+20(7-4) \\ \Rightarrow100+20(3) \\ \Rightarrow100+60 \\ \Rightarrow160 \end{gathered}`

Therefore, the answer is correct.