John, david, and hank are brothers who's ages add to 114 years. john is 10 years older than half of hank's age, while hank is 6 years older than david. what are john, david, and hanks ages?

The answer to your question is:

Hank = 44

John = 32

David = 38

Step-by-step explanation:

Data

John = J

David = D

Hank = H

J + D + H = 114

J = H/2 + 10

H = D + 6

Process

Write the three equations in terms of H

Substitution

                          H/2 + 10 + H - 6 + H = 114

Times 2              H + 20 + 2H - 12 + 2H = 228

                          5H + 8 = 228

                          5H = 228 - 8

                          5H = 220

                          H = 220 / 5

                          H = 44            Hank = 44 years

                    J = 44/2 + 10

                   J = 22 + 10

                   J = 32                 John = 32 years

                          D = 44 - 6

                          D = 38           David = 38 years