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 \(25\) What is the largest number that is on a hat?

Let L , M , N be in increasing order

So....by logic.....

L + M = 11

L + N = 17

M + N = 25

Subtract the first equation from the second

N - M = 6

Add this to the third equation

2N = 31

N = 31/2 = 15.5 = the largest number

And

M = 9.5

L = 1.5