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?

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

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