Question

John is 3 years older than Jim. Jim is 4 years less than half of Dana’s age. How old is each person if their ages add up to 167?

Answer 1

Let’s say John’s age is x. Jim’s age is y. And Dana’s age is z. Then the equation would be:
1.) x + y + z = 167.
We also know that John (x) is 3 years older that Jim (y), so we can make the equation:
2.) y + 3 = x
We know that Jim (y) is 4 years younger than half of Dana’s age (z), so we can make this equation:
3.) z/2 - 4 = y
Now we can combine these equations so that we only have one variable remaining.
The second and third equation can combine to create:
4.) (z/2 - 4) + 3 = x
Then combine the first, third, and fourth equations to have only z as a variable.
5.) ((z/2 - 4) + 3) + (z/2 - 4) + z = 167
Simplify the fifth equation by isolating the variable:
z = 86
Dana’s age is 86. Now plug this into the remaining equations.
86/2 - 4 = 39
Jim is 39. Plug this number into the second equation.
39 + 3 = 42.
John is 42.

FINAL ANSWER:
John = 42
Jim = 39
Dana = 86