help math problem

 

Linda, Miah, and Noah are all wearing hats with numbers on them. Each person adds the two numbers on the other two hats, and they come up with the totals 11, 17, and 28. What is the largest number that is on a hat?  

 

I think you can set it up like this: 

 

Let x stand for the number on one hat  

Let y stand for the number on another hat.  

Let z stand for the number on the final hat. 

 

so     x + y = 11      –>>    y  = 11 – x  

         x + z = 17      –>>    z  = 17 – x  

         y + z = 28  

 

so     y + z = 28       –>>  (11 – x) + (17 – x) = 28  

 

                                          11 – x + 17 – x = 28  

                                           28 – 2x = 28  

                                                – 2x = 0      –>>    x = 0  

 

sub in original expressions    0 + y = 11     –>>    y = 11  

                                              0 + z = 17    –>>     z = 17  

 

so the largest number on a hat is 17  

_.