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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, 19 and 22. What is the largest number that is on a hat?

 Aug 6, 2022
 #1
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 a + b = 11
a + c = 19
b + c = 22 for a, b, c

 

a==4

b==7

c==15

The largest hat number ==15

 Aug 6, 2022
 #2
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Linda: L, Miah: M, Noah: N

L+M = 11. L+N = 19, M+N = 22 or whatever order You place them in.

L = 11 - M, 11 - M + N = 19, so M = N - 8, and so N - 8 + N = 22, or 2N = 30, so N = 15

Going back, we find that M = 15- 10 = 5, and L = 11 - 5 = 6. So the largest number is 15.

 Aug 6, 2022

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