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Algebra Level 3

What value of b b would make the following expression equal to 63?

4 2649 − 4 2646 − 94.5 a 2 5292 − a b \large \frac {4^{2649} - 4^{2646} - 94.5a}{2^{5292} - ab}


The answer is 1.5.

Ashwin Padaki by Ashwin Padaki , 20, USA

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2 solutions

Noel Lo
Jun 14, 2015

4 2649 − 4 2646 − 94.5 a 2 5292 − a b = ( 4 3 − 1 ) ( 4 2646 ) − 94.5 a 2 5292 − a b = ( 64 − 1 ) ( 2 2 ) 2646 − 94.5 a 2 2592 − a b \frac{4^{2649} - 4^{2646} - 94.5a}{2^{5292} - ab} = \frac{(4^3-1)(4^{2646}) - 94.5a}{2^{5292} - ab} = \frac{(64-1)(2^2)^{2646} - 94.5a}{2^{2592} - ab}

= 63 ( 2 5292 ) − 94.5 a 2 5292 − a b = 63 2 5295 − 1.5 a 2 5292 − a b =\frac{63(2^{5292}) - 94.5a}{2^{5292} - ab}= 63\frac{2^{5295} - 1.5a}{2^{5292} - ab}

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Edwin Gray
Sep 14, 2018

4^2649 - 4^2646 = (4^2646)(4^3 - 1) - 94.5 a = 63(2^5292 - ab), or 63 2^5292 - 94.5a = 63*2^5292 - 63ab. cancelling the first term, and multiplying the remainder by -2, 189a = 126ab. Dividing by 63a, b = 3/2 = 1.5. Ed Gray

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