Finding the Two Numbers

Video Explanation

Question

The difference between two numbers is 26 and one number is three times the other. Find the numbers.

Solution

Step 1: Let the Variables

Let the smaller number = \(x\)

Let the larger number = \(y\)

Step 2: Form the Equations

Difference between the numbers:

\[ y – x = 26 \quad (1) \]

One number is three times the other:

\[ y = 3x \quad (2) \]

Step 3: Substitute and Solve

Substitute equation (2) into equation (1):

\[ 3x – x = 26 \]

\[ 2x = 26 \]

\[ x = 13 \]

Step 4: Find the Value of y

\[ y = 3(13) \]

\[ y = 39 \]

Conclusion

Smaller number:

\[ \boxed{13} \]

Larger number:

\[ \boxed{39} \]

Final Answer (For Exam)

The two numbers are 13 and 39.