Ratio, Proportion and Percentages Puzzle – Challenge 30
This is a perfect math puzzle for those who love challenging their brain. The solution is also provided.
![Ratio, Proportion and Percentages Puzzle – Challenge 30](https://www.effortlessmath.com/wp-content/uploads/2020/04/30-512x240.jpg)
Challenge:
The product of two numbers is 216 and their sum is 35. What is their difference?
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![](https://www.effortlessmath.com/wp-content/uploads/2020/04/answer.png)
The correct answer is 19.
Let x be the first number and y the next number. Therefore:
\(xy = 216\) and \(x + y = 35\). Solve the second equation for x:
\(x + y = 35 → x = 35 – y\)
Replace the value of x in the second equation with x in the first equation.
\(xy = 216 → (35 – y) y = 216 →35y – y^2 = 216 →\)
\(y^2 – 35y + 216 = 0\)
Factorize the polynomial: \((y – 8) (y – 27) = 0\)
\(y = 8\) or \(y = 27\)
The difference is 19.
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