Gini-ready.com/student/dashboard/home (1)Ready Marcus collects donations and sends care packages to troops overseas. He has 36 bars of soap and 24 toothbrushes and wants to arrange the items so the packages are identical. What is the greatest number of packages that Marcus can make using all the soap and toothbrushes? (4) What is the greatest number of packages of soap and toothbrushes that Marcus can make? (4arcus can make at most ? packages.

Question

UpStudy AI · Accepted Answer

To determine the greatest number of identical care packages Marcus can create using all 36 bars of soap and 24 toothbrushes, we need to find the **Greatest Common Divisor (GCD)** of the two quantities. The GCD will give us the largest number of packages where both soaps and toothbrushes are distributed evenly.

### Step-by-Step Solution:

1. **List the factors of each number:**
   - **Factors of 36:** 1, 2, 3, 4, 6, 9, 12, 18, 36
   - **Factors of 24:** 1, 2, 3, 4, 6, 8, 12, 24

2. **Identify the common factors:**
   - Common factors of 36 and 24 are **1, 2, 3, 4, 6, 12**

3. **Determine the Greatest Common Divisor (GCD):**
   - The largest common factor is **12**

4. **Calculate the number of items per package:**
   - **Soaps per package:** 36 soaps ÷ 12 packages = **3 soaps per package**
   - **Toothbrushes per package:** 24 toothbrushes ÷ 12 packages = **2 toothbrushes per package**

### **Conclusion:**
Marcus can create **12 identical care packages**, each containing **3 bars of soap** and **2 toothbrushes**.

**Answer:**  
Marcus can make at most **12** identical care packages.
Marcus can make 12 identical care packages, each with 3 bars of soap and 2 toothbrushes.

Real Tutor Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Arithmetic Questions