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JAMB Mathematics 2010 Paper

Question : 21

Total: 49

Find r, if 6r7

_{8}

_{9}

Solution:

Concept:

Convert both numbers to base ten by expanding their place values, then solve for

r

Explanation:

Write the base-8 number in expanded form.

6r7_8 = 6 \times 8^2 + r \times 8^1 + 7 \times 8^0

= 6(64) + r(8) + 7(1)

= 384 + 8r + 7

= 391 + 8r

Write the base-9 number in expanded form.

511_9 = 5 \times 9^2 + 1 \times 9^1 + 1 \times 9^0

= 5(81) + 1(9) + 1(1)

= 405 + 9 + 1

= 415

Set the two values equal.

391 + 8r = 415

8r = 415 - 391

8r = 24

r = \frac{24}{8}

r = 3

Answer:

r = 3

, so the correct option is A.

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