Difference between revisions of "2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 1"
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how much does it cost to monogram SHANA? | how much does it cost to monogram SHANA? | ||
| − | == Solution == | + | == Solution== |
| + | |||
| + | We set up the following equations: | ||
| + | |||
| + | <math>b+r+y+a+n= 21</math> | ||
| + | |||
| + | <math>b+a+2r+y= 25</math> | ||
| + | |||
| + | <math>s+2a+r+h= 18</math> | ||
| + | |||
| + | We are asked to find the price of "Shana", or <math>s+h+2a+n</math>. We notice that this expression has no <math>b</math> or <math>y</math>, so we subtract the first equation from the second to eliminate those variables: | ||
| + | |||
| + | <math>r-n=4</math> | ||
| + | |||
| + | simplfying gets | ||
| + | |||
| + | <math>r=n+4</math> | ||
| + | |||
| + | Which we substitute into the third equation | ||
| + | |||
| + | <math>s+2a+n+4+h=18</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>. | ||
== See also == | == See also == | ||
Revision as of 16:21, 24 July 2016
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:
simplfying gets
Which we substitute into the third equation
.
.
This matches the expression we need to solve for, so we are done. 
.
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 | ||
