If 31410 – 2567 = 340x, find x.

If 314₁₀ – 256₇ = 340_x, find x.

Correct Answer: Option A

Explanation

314₁₀ – 256₇ = 340_x,
Convert 256₇ and 340_x to base 10, such that:
314 – 139 = 3x² + 4x
=> 3x² + 4x – 175 = 0 (quadratic)
Factorising, (x – 7) (3x + 25) = 0,
either x = 7 or x = -25/3 ( but x cannot be negative)
Therefore, x = 7.