Difference between revisions of "1964 AHSME Problems/Problem 11"
Talkinaway (talk | contribs) (Created page with "== Problem== Given <math>2^x=8^{y+1}</math> and <math>9^y=3^{x-9}</math>, find the value of <math>x+y</math> <math>\textbf{(A)}\ 18 \qquad \textbf{(B)}\ 21 \qquad \textbf{(C...") |
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<math>0 = y - 6</math> | <math>0 = y - 6</math> | ||
| + | |||
| + | ==See Also== | ||
| + | {{AHSME 40p box|year=1964|num-b=10|num-a=12}} | ||
| + | |||
| + | [[Category:Introductory Algebra Problems]] | ||
| + | |||
| + | {{MAA Notice}} | ||
<math>y = 6</math> | <math>y = 6</math> | ||
Plugging that back in to <math>x = 3y + 3</math> gives <math>x = 3(6) + 3</math>, or <math>x = 21</math>. Thus, <math>x+y = 21 + 6</math>, or <math>x+y=27</math>, which is option <math>\boxed{\textbf{(D)}}</math> | Plugging that back in to <math>x = 3y + 3</math> gives <math>x = 3(6) + 3</math>, or <math>x = 21</math>. Thus, <math>x+y = 21 + 6</math>, or <math>x+y=27</math>, which is option <math>\boxed{\textbf{(D)}}</math> | ||
Revision as of 11:33, 23 July 2019
Problem
Given 
and 
, find the value of 
Solution
Since 
and 
, we have:
and 
Note that if 
, then 
. Setting the exponents equal gives 
and 
. Plugging the first equation into the second equation gives:
See Also
| 1964 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
Plugging that back in to gives 
, or 
. Thus, 
, or 
, which is option 
