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If $12^2 \cdot 18^3 = 2^x \cdot 3^y$, find $x+y$.

 

THis quesiton was answered by geno before, but i was not sure what to combine. Sorry geno!

Diana can either invest $20,\!000$ dollars for $4$ years with a simple interest rate of $6\%$ or an interest rate of $7\%$ which compounds quarterly. How many more dollars, rounded to the nearest dollar, would she get with the better interest rate?

Guest Dec 14, 2014

Best Answer 

 #1
avatar+17721 
+10

For the second question, the interest rate of 6% yields $24,800.00 while the interest rate of 7% yields $26,398.59.  The question asks how many more dollars the larger yield is than the smaller yield (subtract!).

For the first question:  12²  =  (4·3)2  =  (2·2·3)2  =  (22·3)2  =  24·32

                                    183  =  (2·9)3  =  (2·3·3)3  =  (2·32)3  =  23·36

122·183  =  (24·32)·(23·36)  =  27·38

Since   122·183  = 2x·3y     --->    27·38  =  2x·3y     --->     x = 7   and   y = 8 

There are a lot of steps here; any question?

geno3141  Dec 15, 2014
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1+0 Answers

 #1
avatar+17721 
+10
Best Answer

For the second question, the interest rate of 6% yields $24,800.00 while the interest rate of 7% yields $26,398.59.  The question asks how many more dollars the larger yield is than the smaller yield (subtract!).

For the first question:  12²  =  (4·3)2  =  (2·2·3)2  =  (22·3)2  =  24·32

                                    183  =  (2·9)3  =  (2·3·3)3  =  (2·32)3  =  23·36

122·183  =  (24·32)·(23·36)  =  27·38

Since   122·183  = 2x·3y     --->    27·38  =  2x·3y     --->     x = 7   and   y = 8 

There are a lot of steps here; any question?

geno3141  Dec 15, 2014

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