Question

Real world compositions: A manufacturer sells a lawn mower to a store at $75 over the manufacturing cost. The store then sells the lawn mower for 140% of the price paid to the manufacturer. Determine the function of the price of a lawn mower in terms of the cost to manufacture the mower. What price will a customer pay for this mower if the manufacturer's cost was $230? Solve using composite functions

Answer 1

From the information provided, the lawn mower is sold at a price which is $75 over the cost of manufacture.

If the cost of manufacture is x, then we would have;

`f(x)=x+75`

Also, the store now sells the lawn mower for 140% of the price paid to the manufacturer. Therefore, we would have;

`g(x)=f(x)1.4`

Hence, if the manufacturer's cost is $230, the customer would be paying g(x). When the cost x is now given as 230, we wou;d have;

`\begin{gathered} f(230)=230+75 \\ f(230)=305 \\ \text{Hence;} \\ g(x)=f(x)1.4 \\ g(x)=305*1.4 \\ g(x)=427 \end{gathered}`

ANSWER:

The function of the price is;

`f(x)=x+75`

The price a customer pays when the cost of manufacturing is $230 would now be $427