Three years ago, Jim was half as old as Tom. Three years from now, Jim will be half as old as Michael. If Jim's age now is half as old as Michael's age three years ago, How old are Jim, Tom and Michael at present?
Just translate the words to symbols:
j-3 = (t-3)/2
j+3 = (m+3)/2
j = (m-3)/2
Unfortunately, those three equations do not determine their ages uniquely.
Jim,Tom,Michael could be
4,5,11
5,7,13
6,9,15
. . .
I suspect a typo in the problem.
To solve this problem, we can break it down into steps and use algebra to find the ages of Jim, Tom, and Michael.
Step 1: Assign variables
Let's assign variables to the ages of Jim, Tom, and Michael.
- Let's say Jim's age is J.
- Tom's age would then be T.
- Michael's age would be M.
Step 2: Translate the information into equations
Based on the given information, we can create three equations.
Three years ago, Jim was half as old as Tom:
J - 3 = (1/2)(T - 3) Equation 1
Three years from now, Jim will be half as old as Michael:
J + 3 = (1/2)(M + 3) Equation 2
Jim's age now is half as old as Michael's age three years ago:
J = (1/2)(M - 3) Equation 3
Step 3: Solve the equations simultaneously
Now we can solve these equations to find the values of J, T, and M.
From Equation 3, we can simplify and write J in terms of M:
J = (1/2)(M - 3)
Substituting this expression for J in Equations 1 and 2:
(1/2)(M - 3) - 3 = (1/2)(T - 3)
(1/2)(M - 3) + 3 = (1/2)(M + 3)
Let's simplify these equations:
(M - 3) - 6 = (T - 3) Multiplying both sides of Equation 1 by 2 and simplifying.
(M - 3) + 6 = (1/2)(M + 3) Multiplying both sides of Equation 2 by 2 and simplifying.
Simplifying both equations:
M - 9 = T - 3 Equation 4
M + 3 = (1/2)M + 3/2 Equation 5
Now, let's solve Equation 4 for T:
T = M - 6 Equation 6
Substituting Equation 6 into Equation 5:
M + 3 = (1/2)M + 3/2
Multiplying both sides of the equation by 2 to get rid of the fraction:
2M + 6 = M + 3
Simplifying further:
M = -3
Substituting the value of M back into Equation 6:
T = (-3) - 6
T = -9
Based on these results, we have found the ages of Jim, Tom, and Michael to be:
Jim (J): -3 years old
Tom (T): -9 years old
Michael (M): -3 years old
However, negative ages do not make sense in this context. So, it seems there was an error in the given information or the problem itself. Please double-check the given ages or provide any additional information if available.