Question

Rachel wants to buy a bike for $300 dollars. She currently has $150 and is saving $10 each week. The bike owner is decreasing the price of the bike $15 every week he doesn’t sell it. How many weeks until Rachel has enough money to buy the bike?

Answer 1

The given information is:

The price of the bike is $300 and its price is decreasing $15 every week.

Rachel currently has $150 and is saving $10 each week.

We can find the price of the bike with the following equation:

`P(w)=300-15(w-1)`

Where w is the number of weeks.

And the money Rachel has is given by:

`M(w)=150+10w`

To find how many weeks until Rachel has enough money to buy the bike, we need to equal both equations and solve for w:

`\begin{gathered} P(w)=M(w) \\ 300-15(w-1)=150+10w \\ 300-150-15w+15=10w \\ 165-15w=10w \\ 165=10w+15w \\ 165=25w \\ (165)/(25)=w \\ 6.6=w \end{gathered}`

There are needed 7 weeks, because the first week Rachel has 150+10, and it increases 10 each week, but the price of the bike decreases on week 2, because the bike owner is decreasing the price every week he doesn't sell it, then he starts on week 2.