Chapter 8.1, Problem 19PPSE

Solution

a.

To state: The function that relates the sales and the number of muffins if the given table shows the number of muffins sold and the amount of sales.

Number of Muffins (m)	Sales (s)
5	$12.50
8	$20.00
13	$32.50
20	$50.00

The resultant function is $s=2.5m$ .

Given information:

The given table is:

Number of Muffins (m)	Sales (s)
5	$12.50
8	$20.00
13	$32.50
20	$50.00

Explanation:

To find the function that relates the sales and the number of muffins, first find the relation between the sales and the number of muffins.

From the table it can be seen that:

  $\frac{12.5}{5}=2.5,\frac{20}{8}=2.5,\frac{32.50}{13}=2.5,\frac{50.00}{20}=2.5$

From the above result it can be observed that $m\text{and}s$ are in direct proportion.

Then,

  $\begin{array}{c}\frac{s}{m}=2.5\\ s=2.5m\end{array}$

Therefore, the function that relates the sales and the number of muffins is $s=2.5m$ .

b.

To state: The number of muffins that are to be sold to make at least $250.00 in sales.

The resultant answer is at least 100 muffins.

Given information:

From part (a), the function that relates the sales and the number of muffins is $s=2.5m$ .

Explanation:

The function that relates the sales and the number of muffins is $s=2.5m$ .

To find the number of muffins that is to be sold to make at least $250.00 in sales, substitute the value of s as $250.00 in the function $s=2.5m$ .

  $\begin{array}{c}s=2.5m\\ 250=2.5m\\ \frac{250}{2.5}=m\\ 100=m\end{array}$

Therefore, 100 muffins must be sold to make at least $250.00 in sales.