Difference between revisions of "2013 AMC 8 Problems/Problem 15"
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If <math>3^p + 3^4 = 90</math>, <math>2^r + 44 = 76</math>, and <math>5^3 + 6^s = 1421</math>, what is the product of <math>p</math>, <math>r</math>, and <math>s</math>? | If <math>3^p + 3^4 = 90</math>, <math>2^r + 44 = 76</math>, and <math>5^3 + 6^s = 1421</math>, what is the product of <math>p</math>, <math>r</math>, and <math>s</math>? |
Revision as of 21:46, 11 November 2017
Problem
If ,
, and
, what is the product of
,
, and
?
Solution
First, we're going to solve for . Start with
. Then, change 3^4 to
. Subtract
from both sides to get
and see that
is
. Now, solve for
. Since
,
must equal
, so
. Now, solve for
.
can be simplified to
which simplifies further to
. Therefore,
.
equals
which equals
. So, the answer is
.
See Also
2013 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.