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.

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.