Math Problem Statement

The sum of two numbers is 52. One number is 3 times as large as the other. What are the numbers?

Solution

The problem in the image can be translated into two equations. Here's how to set it up:

Let:

  • xx be the smaller number.
  • 3x3x be the larger number (since one number is 3 times as large as the other).

The sum of the two numbers is 52: x+3x=52x + 3x = 52

Now, solve for xx: 4x=524x = 52 x=524=13x = \frac{52}{4} = 13

Thus:

  • The smaller number is 1313.
  • The larger number is 3×13=393 \times 13 = 39.

The numbers are 13 and 39.

Would you like more details or have any questions?

Here are 5 related questions to consider:

  1. How do you form equations based on word problems?
  2. What happens if the relationship between the numbers is different (e.g., one number is twice as large)?
  3. How would the equation change if the sum of the numbers was different?
  4. Can you create a similar problem but with different relationships between the numbers?
  5. How do you verify the solution in such problems?

Tip: Always check your solutions by substituting the values back into the original problem to ensure they satisfy all conditions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

x + 3x = 52

Theorems

Basic equation solving in algebra

Suitable Grade Level

Grades 6-8