Solving a system of equations, we conclude that the largest number on a hat is 14.
What is the largest number on a hat?
We have 3 hats, each one with a number that we will define as:
x, y, and z.
We know that by adding pairs of these numbers we get 11, 17 and 22, then we can write a system of equations:
x + y = 11
x + z = 17
y + z = 22
Clearly z is the largest number, so we want to find z.
First, we can isolate x on the first equation so we get:
x = 11 - y
Replacing that in the second equation giveS:
x + z = 17
(11 - y) + z = 17
Now our system is:
y + z = 22
(11 - y) + z = 17
Isolating y in the first one we get:
y = 22 - z
Now we can replace that in the other equation:
(11 - (22 - z)) + z = 17
Now we can solve this for z.
11 - 22 + z + z = 17
-11 + 2z = 17
2z = 17 + 11 = 28
z = 28/2 = 14
z = 14
We conclude that the largest number on a hat is 14.
If you want to learn more about systems of equations:
https://brainly.com/question/13729904
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