Chapter CSB1.2, Problem 29E

a.

To determine

The longest possible piece if all are cuts into same length.

Answer to Problem 29E

The longest possible piece of equal length is 4 inch.

Explanation of Solution

Given:

The length of two sandwiches are 16 inch and 28 inch.

Since, the two sandwiches are cut into various pieces of same length.

Then, the longest possible piece will be the HCF of length of both sandwiches.

i.e. Longest piece = HCF (16, 28)

As HCF of 16 and 28 is 4.

So the longest possible piece of equal length is 4 inch.

b.

To determine

Total number of pieces.

Answer to Problem 29E

The total number of piece is $n=11$

Explanation of Solution

Given:

The length of two sandwiches are 16 inch and 28 inch.

Since from the previous subpart, the longest possible piece of equal length is 4 inch.

So, the total number of piece is

  $\begin{array}{l}n=\frac{16}{4}+\frac{28}{4}\\ \Rightarrow n=11\end{array}$