SOLUTION: Jimmy is 6 years older than Tom. In three years time Jimmy will be twice as old as Tom. How old is Jimmy now. Show all calculations

Question 1057171: Jimmy is 6 years older than Tom. In three years time Jimmy will be twice as old as Tom. How old is Jimmy now. Show all calculations
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
t = Tom's age
j = Jimmy's age
j = t+6 ("Jimmy is 6 years older than Tom")
j+3 = 2(t+3) ("In three years Jimmy will be twice as old as Tom)

We want to solve for j, so re-arrange the top eqn to t = j-6 then substitute the right hand side for "t" in the bottom equation, that will give us one equation with just 'j's and we should be able to solve for j:
j+3 = 2((j-6)+3) (substituted "j-6" for "t" in 2nd eqn)
j+3 = 2(j-3) (combined -6 and +3)
j+3 = 2j-6 (multiplied the 2 into paren's)
9 = j (added 6 to both sides, subtracted j from both sides)
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Ans: Jimmy is 9 years old
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Check: Jimmy is 9 �> Tom is 3 (from problem statement or re-arranged top eqn)
In 3 years, Jimmy will be 12 and Tom will be 6 (so Jimmy will be 2x Tom's age)

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