Chapter 4.2, Problem 66E

To determine

To find the greatest number of identical first aid kits that could be made out of given items..

Answer to Problem 66E

3 kits; 16 bandages, 5 squares of gauze, 3 tubes of antibiotic ointments and 3 packs of ice for each first aid kit.

Explanation of Solution

Given Information: 48 bandages, 15 squares of gauze, 6 tubes of antibiotic ointment and 6 ice packs.

Formula used: Find the greatest prime factor of the four items using factorization method.

Calculation:

The factors of 6 tubes of ointment are: 1, 2, 3, 6

The factors of 6 ice packs are: 1, 2, 3, 6

The factors of 15 squares of gauze are: 1, 3, 5, 15

The factors of 48 bandages are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Then the greatest common factor for the 4 items is 3.

Therefore, a maximum of 3 identical kits could be made out of 48 bandages, 15 squares of gauze, 6 tubes of antibiotic ointment and 6 ice packs.

Now, to find the number of items each kit will contain divide the total number of kits(i.e. GCF) with each number of items.

For bandages $\frac{bandages}{kits}=\frac{48}{3}=16$

• 16 bandages.
• For gauze: $\frac{gauze}{kits}=\frac{15}{3}=5$

5 squares of gauze

• For antibiotic ointment: $\frac{tubes}{kits}=\frac{9}{3}=3$

3 tubes of antibiotic ointments

• For ice packs: $\frac{icepacks}{kits}=\frac{6}{3}=2$

3 packs of ice