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The problem states:

"Jabari is thinking of three numbers. The greatest number is twice as large as the least number. The middle number is three more than the least number. The sum of the three numbers is 75. Find the numbers."

### Step 1: Define a variable
Let:
- \( x \) = the least number.

Then, based on the problem:
- The middle number = \( x + 3 \) (3 more than the least number).
- The greatest number = \( 2x \) (twice as large as the least number).

### Step 2: Set up the equation
The sum of the three numbers is 75, so:
\[
x + (x + 3) + 2x = 75
\]

### Step 3: Solve the equation
Simplify the left-hand side:
\[
x + x + 3 + 2x = 75
\]
\[
4x + 3 = 75
\]
Subtract 3 from both sides:
\[
4x = 72
\]
Divide by 4:
\[
x = 18
\]

### Step 4: Find the other numbers
- The least number is \( x = 18 \).
- The middle number is \( 18 + 3 = 21 \).
- The greatest number is \( 2 \times 18 = 36 \).

### Step 5: Check the solution
The sum of the numbers is:
\[
18 + 21 + 36 = 75
\]
Thus, the solution is correct.

### Final Answer:
The three numbers are **18, 21, and 36**.

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Would you like further details or have any questions?

Here are some related questions:
1. How would the equation change if the middle number was 5 more than the least?
2. What if the greatest number was three times the least instead of twice?
3. How can you verify if your solution is correct without recalculating the sum?
4. What if the sum of the numbers was 90 instead of 75?
5. How does defining a variable help simplify the problem-solving process?

**Tip:** When solving word problems, always break them down into smaller parts to avoid confusion.

Jabari is thinking of three numbers. The greatest number is twice as large as the least number. The middle number is three more than the least number. The sum of the three numbers is 75. Find the numbers.

Solve a problem where three numbers have specific relationships: the greatest is twice the least, the middle is three more than the least, and their sum is 75. A step-by-step algebraic solution is provided, suitable for Grades 6-8.

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