Finely proportioned

Algebra Level 2

Let x x be a real number such that x < 30 x < 30

32 : x : : x : ( 2 x − 27 ) 32 : x :: x : (2x-27)

Find x x to 2 decimal places.

Note: The symbol : : :: denotes that the 2 ratios are equivalent.


The answer is 19.35.

Denton Young by Denton Young , 47, USA

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1 solution

Denton Young
Apr 20, 2017

By rule of proportions, x × x = 32 × ( 2 x − 27 ) x \times x = 32 \times (2x-27)

Simplifying, x 2 − 64 x + 864 = 0 x^2 - 64x + 864 =0

Solving via quadratic formula, x = 32 + 160 x = 32 + \sqrt{160} or x = 32 − 160 x = 32 - \sqrt{160}

Since x < 30 x < 30 , we use the second solution.

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