Chapter 3.5, Problem 11CYU

a.

To determine

A function $n(p)$ which represents the cost of the paints with the 15% discount

Answer to Problem 11CYU

  $n(p)=5.9415p$

Explanation of Solution

Given:

  $f(p)=6.99p$

Where, p is the number of paints bought.

  $f(p)$ represents the total cost of paint bought without any discount.

Calculation:

Now, when 15% discount is allowed on the total purchase,

  $\begin{array}{l}\Rightarrow n(p)=f(p)-\frac{15}{100}f(p)\\ \Rightarrow n(p)=0.85f(p)\\ \Rightarrow n(p)=0.85\times 6.99p\\ \Rightarrow n(p)=5.9415p\end{array}$

Conclusion:

Hence, the total cost after allowing 15% discount is: $n(p)=5.9415p.$

b.

To determine

The cost of 5 paints before and after discount

Answer to Problem 11CYU

Before discount the cost of 5 paints is 34.95.

After discount the cost of 5 paints is 29.7075

Explanation of Solution

Given:

  $f(p)=6.99p$

  $n(p)=5.9415p$

Calculation:

Now, 5 paints were bought, which means p=5.

The total cost of paint bought without any discount,

  $f(5)=6.99\times 5=34.95$

The total cost of paint bought with 15% discount is

  $n(5)=5.9415\times 5=29.7075$

Conclusion:

Hence, the total cost before discount is 34.95 and after discount is 29.7075.