Difference between revisions of "UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 1"
Hashtagmath (talk | contribs) m (→Credits) |
(→Solution) |
||
Line 28: | Line 28: | ||
This matches the expression we need to solve for, so we are done. <math>\boxed{14}</math>. | This matches the expression we need to solve for, so we are done. <math>\boxed{14}</math>. | ||
+ | |||
+ | |||
+ | ==Solution 2== | ||
+ | Notice that BRYAN is simple BARRY rearranged, and SARAH is simple SHANA rearranged. Let the cost of rearranging SHANA be <math>x</math>. We have the following equation: | ||
+ | <cmath>21+18=25+x</cmath> | ||
+ | Solving for <math>x</math>, our answer is <math>\boxed{14}</math>. | ||
==Credits== | ==Credits== |
Revision as of 23:43, 3 August 2020
Contents
Problem
Four siblings BRYAN, BARRY, SARAH and SHANA are having their names monogrammed on their towels. Different letters may cost different amounts to monogram. If it costs to monogram BRYAN, to monogram BARRY and to monogram SARAH, how much does it cost to monogram SHANA?
Solution
We set up the following equations:
We are asked to find the price of "Shana", or . We notice that this expression has no or , so we subtract the first equation from the second to eliminate those variables:
Which we substitute into the third equation
.
.
This matches the expression we need to solve for, so we are done. .
Solution 2
Notice that BRYAN is simple BARRY rearranged, and SARAH is simple SHANA rearranged. Let the cost of rearranging SHANA be . We have the following equation: Solving for , our answer is .
Credits
- Credit to Football017 for writing the solution
See also
2014 UNM-PNM Contest II (Problems • Answer Key • Resources) | ||
Preceded by First Question |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNM-PNM Problems and Solutions |