Whole Numbers Word problem involving the least common multiple of 2 numbers $$ \square \square \square \square \square \square \square \square \square $$ 0/5 Español Ahmad sells boxes of cookies for $$ \$ 10 $$ each. Carmen sells boxes of cookies for $$ \$ 8 $$ each. Each of them sold the same dollar amount. It was the smallest dollar amount for which this was possible. Answer the following questions. What was the dollar amount each of them sold? $$ \square $$ How many boxes did Ahmad sell? $$ \square $$ boxes How many boxes did Carmen sell? $$ \square $$ boxes Explanation Check © 2025 McGraw Hill LLC. All Rights Reserved. Terms of Use I Privacy Center I Accessibility

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UpStudy AI · Accepted Answer

To solve the problem, we need to find the least common multiple (LCM) of the prices of the boxes of cookies sold by Ahmad and Carmen. Ahmad sells boxes for $$ \$10 $$ each, and Carmen sells boxes for $$ \$8 $$ each.

### Step 1: Find the LCM of 10 and 8

The LCM of two numbers is the smallest number that is a multiple of both. We can find the LCM by listing the multiples of each number or using the prime factorization method.

- **Prime factorization:**
  - $$ 10 = 2 \times 5 $$
  - $$ 8 = 2^3 $$

To find the LCM, we take the highest power of each prime factor:
- For $$ 2 $$: the highest power is $$ 2^3 $$ (from 8).
- For $$ 5 $$: the highest power is $$ 5^1 $$ (from 10).

Thus, the LCM is:
$$
\text{LCM} = 2^3 \times 5^1 = 8 \times 5 = 40
$$

### Step 2: Determine the dollar amount each of them sold

The smallest dollar amount for which both Ahmad and Carmen sold the same amount is $$ \$40 $$.

### Step 3: Calculate the number of boxes sold by each

- **For Ahmad:**
  $$
  \text{Number of boxes sold by Ahmad} = \frac{40}{10} = 4 \text{ boxes}
  $$

- **For Carmen:**
  $$
  \text{Number of boxes sold by Carmen} = \frac{40}{8} = 5 \text{ boxes}
  $$

### Summary of Answers

1. What was the dollar amount each of them sold?
   - $$ 40 $$

2. How many boxes did Ahmad sell?
   - $$ 4 $$ boxes

3. How many boxes did Carmen sell?
   - $$ 5 $$ boxes

Thus, the final answers are:
- Dollar amount: $$ 40 $$
- Ahmad's boxes: $$ 4 $$
- Carmen's boxes: $$ 5 $$
Each sold \$40. Ahmad sold 4 boxes, and Carmen sold 5 boxes.

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