Ratio, Proportion and Percentages Puzzle – Challenge 30

Challenge:

The product of two numbers is 216 and their sum is 35. What is their difference?

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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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