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