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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?

 Apr 8, 2022
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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?    

 

When "a" looks at the other two, she sees 11, so let's say b + c = 11  

When "b" looks at the other two, she sees 17, so let's say a + c = 17  

When "c" looks at the other two, she sees 28, so let's say a + b = 28   

 

From there, it's just substitution.  Get a in terms of c  —>    a = 17 – c 

                                                    Get b in terms of c  —>    b = 11 – c  

 

Substitute these terms into a + b = 28                    (17 – c) + (11 – c) = 28  

                                                                                    17 – c + 11 – c = 28   

                                                                                               28 – 2c = 28  

                                                                                                    – 2c = 0  

                                                                                                         c = 0  

 

Substitute value of c into b + c = 11                                            b + 0 = 11  

                                                                                                         b = 11  

 

Substitute value of c into a + c = 17                                            a + 0 = 17   

                                                                                                          a = 17   

 

So, the largest number on a hat is 17   

.

 Apr 8, 2022

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