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JAMB Mathematics 2015 Paper

Question : 27

Total: 61

Find x if 132_x = 70 _eight.

Solution:

Concept:

Convert both numbers to base 10 and solve for

x

Explanation:

Write

132_x

in base 10:

132_x = 1 \times x^2 + 3 \times x^1 + 2 \times x^0 = x^2 + 3x + 2

Write

70_{\text{eight}}

in base 10:

70_{\text{eight}} = 7 \times 8^1 + 0 \times 8^0 = 56

Equate the two expressions:

x^2 + 3x + 2 = 56

Simplify:

x^2 + 3x - 54 = 0

Factorise the quadratic:

(x + 9)(x - 6) = 0

x = -9

x = 6

A base must be positive and greater than any digit used, so

x = 6

Answer:

x = 6

Option C.

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