The difference between two numbers is 14, and their product is 120. What is the smaller number?

Thu, 07 May 2026 07:10:30 +0000

**Why the difference between two numbers is 14, and their product is 120 still surprises math learners in 2025**
Math puzzles like “the difference between two numbers is 14, and their product is 120 — what is the smaller number?” are far more than a playground riddle. In a time when curiosity-driven education thrives, especially on platforms like Discover, this question sparks thoughtful engagement among viewers exploring logic, algebra, and numeracy. With growing interest in STEM basics and problem-solving apps, this type of equation is surfacing organically as users seek clear, curiosity-driven answers—without venture capital flair or unsolicited advice. The equation — difference of 14, product of 120 — reveals a quiet consistency in numerical relationships, offering insight into how integers shape mathematical patterns. Solving for the smaller number isn’t just about plugging in values; it’s a gateway to deeper reasoning about equations and real-world applications in budgeting, planning, or data analysis. ### Why this numerical mystery is gaining traction in the US
This question reflects a broader shift: the U.S. audience increasingly values clear, evidence-based explanations over flashy content. As students prepare for academic challenges, careers in tech or finance sharpen analytical thinking, and parents explore learning tools—equations like this serve as accessible entry points. Moments of curiosity peak on mobile devices, especially during evening screen time, when users seek low-pressure mental exercises. The simplicity of the setup—diff + product given—makes it ideal for Discover’s intent-driven timeline, where learners want quick clarity with room to explore further. ### How this equation actually works: a step-by-step breakdown
To find the smaller number, begin with algebra. Let the two numbers be \( x \) and \( x + 14 \) (since difference is 14). Their product is 120:
\( x(x + 14) = 120 \)
Expanding gives:
\( x^2 + 14x - 120 = 0 \)
Using the quadratic formula:
\( x = \frac{-14 \pm \sqrt{14^2 - 4(1)(-120)}}{2(1)} = \frac{-14 \pm \sqrt{196 + 480}}{2} = \frac{-14 \pm \sqrt{676}}{2} \)
Since \( \sqrt{676} = 26 \),
\( x = \frac{-14 \pm 26}{2} \)
This yields two solutions:
\( x = \frac{12}{2} = 6 \), and \( x = \frac{-40}{2} = -20 \)
Only positive numbers align with real-world expectations here; \( x = 6 \) and \( x + 14 = 20 \) confirm both conditions: difference = 14, product = 120.