Chapter 8.1, Problem 26P

A local deli kept track of the sandwiches it sold for three months. The polynomials below model the number of sandwiches sold, where $s$ represents days.

Ham and Cheese: $4s^3-28s^2+33s+250$

$\text{ Pastrami: }-7.4s^2+32s+180$

Write a polynomial that models the total number of these sandwiches that were sold.

To determine

To find: a polynomial that models the total number of sandwiches that were sold

Answer to Problem 26P

  $4s^3-35.4s^2+65s+430$ denotesapolynomial that models the total number of sandwiches that were sold

Explanation of Solution

Given information: Polynomial that denotes number of Ham and Cheese sandwiches sold is $4s^3-28s^2+33s+250$

Polynomial that denotes number of Pastrami sandwiches sold is $-7.4s^2+32s+180$

Calculation:

Polynomial that denotes number of Ham and Cheese sandwiches sold $=4s^3-28s^2+33s+250$

Polynomial that denotes number of Pastrami sandwiches sold $=-7.4s^2+32s+180$

To find a polynomial that models the total number of sandwiches that were sold, add Polynomial that denotes number of Ham and Cheese sandwiches sold and Polynomial that denotes number of Pastrami sandwiches sold

Therefore,

Polynomial that models the total number of sandwiches that were sold $=\left(4s^3-28s^2+33s+250\right)+\left(-7.4s^2+32s+180\right)$

  $\begin{array}{l}=4s^3-28s^2+33s+250-7.4s^2+32s+180\\ =4s^3+\left(-28s^2-7.4s^2\right)+(33s+32s)+(250+180)\\ =4s^3-35.4s^2+65s+430\end{array}$