Chapter CSB1.2, Problem 34E

a.

To determine

The longest length that T can cut so that he can have paper streamers of all colors having same length.

Answer to Problem 34E

24 inches.

Explanation of Solution

Given information:

Length of blue roll = 144 in.

Length of red roll = 192 in.

Length of yellow roll = 360 in.

Calculation:

The longest length that he can cut will be equal to GCF of 144, 192 and 360.

Now, prime factors of 144, 192 and 360 are

  $\begin{array}{l}144=2\times 2\times 2\times 2\times 3\times 3\\ 192=2\times 2\times 2\times 2\times 2\times 2\times 3\\ 360=2\times 2\times 2\times 3\times 3\times 5\end{array}$

Therefore GCF of 144, 192 and 360 = $2\times 2\times 2\times 3=24$

Hence longest length will be 24 inches.

b.

To determine

The number of total streamers T will have.

Answer to Problem 34E

6

Explanation of Solution

Given information:

Length of blue roll = 144 in.

Length of red roll = 192 in.

Length of yellow roll = 360 in.

Calculation:

Number of streamers will be:

  $=\frac{\text{lenght of smallest color roll}}{\text{lenght of each streamer}}$

  $=\frac{144}{24}=6$