SOLUTION: Bill is 6 years older than Tom. Three years ago, Bill's age was four times Tom's age. What are the boys ages now? How do I write this in a single variable equation? I have tried {{

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Question 375011: Bill is 6 years older than Tom. Three years ago, Bill's age was four times Tom's age. What are the boys ages now? How do I write this in a single variable equation? I have tried +%28x+%2B+6%29-3+=+4%28x-3%29 and a-3=4%28a-6%29-3 I have gotten this wrong on two different quizzes, so I am curious what the correct answer is?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let B = bill's age now, T = Tom's age now


So Bill's age 3 yrs ago was B-3 and Tom's age 3 yrs ago was T-3


Since "Bill is 6 years older than Tom", we know that B=T%2B6


Also, because "Bill's age was four times Tom's age", we know that B-3=4%28T-3%29


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B-3=4%28T-3%29 Start with the second equation.


T%2B6-3=4%28T-3%29 Plug in B=T%2B6 (ie replace each 'B' with 'T+6'). So this would be the starting point of the single variable equation you're looking for.


T%2B6-3=4T-12 Distribute.


3%2BT=4T-12 Combine like terms on the left side.


T=4T-12-3 Subtract 3 from both sides.


T-4T=-12-3 Subtract 4T from both sides.


-3T=-12-3 Combine like terms on the left side.


-3T=-15 Combine like terms on the right side.


T=%28-15%29%2F%28-3%29 Divide both sides by -3 to isolate T.


T=5 Reduce.


So this means that Tom is 5 yrs old.


Now plug this value into B=T%2B6 to get B=5%2B6=11. So B=11 which means that Bill is 11 yrs old.


Notice that 3 yrs ago, Bill was 11-3=8 yrs old and Tom was 5-3=2 years old. Also notice that 8 is 4 times 2.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim