2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 1
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?
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. .
BRYAN, SARAH is an anagram of BARRY, SHANA. Let SHANA be . So we have the following equation:
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