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Emanuel wants to save $600 to buy a TV. He saves 18 each week. The amount A (in dollars) that he still needs after w weeks is given by the following function.A (w) = 600-18w

Emanuel Wants To Save 600 To Buy A TV He Saves 18 Each Week The Amount A In Dollars That He Still Needs After W Weeks Is Given By The Following FunctionA W 6001 class=

Sagot :

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

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