Alice is 3 years old. nate is half of the sum of alice's age and 5. how old is nate?

 The required age of Nate is 4 years.

Step-by-step explanation:  Given that Alice is 3 years old and Nate is half of the sum of Alice's age and 5.

We are to find the age of Nate.

Let x and y represents the ages of Alice and Nate respectively in years.

Then, according to the given information, we have

and also,

Thus, the required age of Nate is 4 years.

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x