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

## 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. $\boxed{14}$.

## Credits

• Credit to Football017 for writing the solution

 2014 UNM-PNM Contest II (Problems • Answer Key • Resources) Preceded byFirst Question Followed byProblem 2 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 All UNM-PNM Problems and Solutions