We have been given that the formula that defines the amount A (in dollars) that he still needs after w weeks is given by the following function.
[tex]A(w)=600-18w[/tex]Part A
We are told to find how much money Manuel still needs after 7 weeks. To do this, we will simply substitute w=7
[tex]\begin{gathered} A(7)=600-18\times7 \\ A(7)=600-126 \\ A(7)=\text{ \$474} \end{gathered}[/tex]Emmanuel still needs to save $474
Part B
We are told to find the number of weeks Emanuel has been saving if he still needs $294.
To do this we will simply substitute A(w) =294 and solve for w.
So that
[tex]294=600-18w[/tex]To solve this, we will collect like terms
[tex]\begin{gathered} 18w=600-294 \\ 18w=306 \end{gathered}[/tex]
Dividing both sides by 18
[tex]\begin{gathered} \frac{18w}{18}=\frac{306}{18} \\ \\ w=17 \end{gathered}[/tex]This means that Emmanuel has been saving for 17 weeks