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Difference between revisions of "2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 1"

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<math>r-n=4</math>
 
<math>r-n=4</math>
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simplfying gets
 
  
 
<math>r=n+4</math>
 
<math>r=n+4</math>
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<math>s+2a+n+4+h=18</math>.
 
<math>s+2a+n+4+h=18</math>.
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<math>s+2a+n+h=14</math>.
 
<math>s+2a+n+h=14</math>.
  
 
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>.
 +
 +
 +
==Slick Solution==
 +
BRYAN, SARAH is an anagram of BARRY, SHANA. Let SHANA be <math>x</math>. So we have the following equation:
 +
<cmath>21+18=25+x\rightarrow \boxed{x=14}</cmath>
 +
 +
~yofro
  
 
== See also ==
 
== See also ==

Latest revision as of 11:55, 4 August 2020

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 $\textdollar{21}$ to monogram BRYAN, $\textdollar{25}$ to monogram BARRY and $\textdollar{18}$ to monogram SARAH, how much does it cost to monogram SHANA?

Solution

We set up the following equations:

$b+r+y+a+n= 21$

$b+a+2r+y= 25$

$s+2a+r+h= 18$

We are asked to find the price of "Shana", or $s+h+2a+n$. We notice that this expression has no $b$ or $y$, so we subtract the first equation from the second to eliminate those variables:

$r-n=4$

$r=n+4$

Which we substitute into the third equation

$s+2a+n+4+h=18$.

$s+2a+n+h=14$.

This matches the expression we need to solve for, so we are done. $\boxed{14}$.


Slick Solution

BRYAN, SARAH is an anagram of BARRY, SHANA. Let SHANA be $x$. So we have the following equation: \[21+18=25+x\rightarrow \boxed{x=14}\]

~yofro

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
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