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2000

Mathematics

67ca00ce0c643c71d77dee1f

If 31410 - 2567 = 340x, find x.

A.

7

B.

8

C.

9

D.

10

Correct Answer: 7

Explanation

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.

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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