The sum of two numbers is 44. One of the numbers is 3 times as large as the other. What are the two numbers?

Introduction:
This is a very common linear equation word problem. You are told the sum of two numbers and that one number is three times the other. These conditions are enough to form and solve a simple algebraic equation. Problems like this strengthen basic algebra skills and help with quick mental modeling of relationships between numbers.

Given Data / Assumptions:

• The sum of the two numbers is 44.
• One number is 3 times as large as the other.
• Let the smaller number be x and the larger number be 3x.

Concept / Approach:
Set up an equation using the sum condition: x + 3x = 44. Solve this simple equation for x, then multiply by 3 to get the larger number. Finally, present both numbers as a pair in ascending or logical order.

Step-by-Step Solution:
Let the smaller number be x.Then the larger number is 3x.Given: x + 3x = 44.4x = 44.x = 44 / 4 = 11.Larger number = 3 * 11 = 33.So the two numbers are 11 and 33.

Verification / Alternative check:
Check the sum: 11 + 33 = 44, correct. Check the relationship: 33 is indeed 3 times 11. Both conditions are satisfied exactly, so the solution (11, 33) is correct.

Why Other Options Are Wrong:
4 and 40: sum is 44 but 40 is 10 times 4, not 3 times.3 and 41: sum is 44 but 41 is not 3 times 3.10 and 34 or 12 and 32: both pairs have sum 44, but the larger numbers are not 3 times their smaller counterparts.

Common Pitfalls:
Confusing which number is three times the other and setting up reversed equations.Trying to guess pairs instead of writing the straightforward equation x + 3x = 44.Arithmetic mistakes when dividing 44 by 4.

Final Answer:
11 and 33