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WAEC Mathematics 2016 Paper

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Question : 1

Total: 49

If 23_x + 101_x = 130_x, find the value of x

7
6
5
4

Solution:

Concept:

Convert numbers in base

x

to powers of

x

, then solve the linear equation.

Explanation:

Write

23_x

as

2x + 3

.

Write

101_x

as

x^2 + 1

.

Write

130_x

as

x^2 + 3x

.

So,

(2x + 3) + (x^2 + 1) = x^2 + 3x

.

Simplify:

x^2 + 2x + 4 = x^2 + 3x

.

Cancel

x^2

from both sides:

2x + 4 = 3x

.

Therefore,

x = 4

.

Answer:

x = 4

, so the correct option is D.

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