Question

If the difference of two numbers is 26 and one number be three times the other, then find the numbers.

Hint:

Translate word problems into equations using variables, then solve systematically.

Answer 1

Step 1: Let the smaller number be \(x\).
Then, the larger number will be \(3x\).
Step 2: Apply the condition given.
\[ 3x - x = 26 \implies 2x = 26 \implies x = 13 \]
Step 3: Find both numbers.
Smaller number \(= 13\), Larger number \(= 3x = 39\).
Step 4: Conclusion.
Hence, the two numbers are \(\boxed{13 \text{ and } 39}\).