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If 31410 - 2567 340x find x - JAMB Mathematics 2000 Question

If 31410 - 2567 = 340x, find x.
A
7
B
8
C
9
D
10
correct option: a

31410 - 2567 = 340x,

Convert 2567 and 340x 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.

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