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 and I have gotten this wrong on two different quizzes, so I am curious what the correct answer is?
Answer by jim_thompson5910(35256) (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 and Tom's age 3 yrs ago was
Since "Bill is 6 years older than Tom", we know that
Also, because "Bill's age was four times Tom's age", we know that
-------------------------
Start with the second equation.
Plug in (ie replace each 'B' with 'T+6'). So this would be the starting point of the single variable equation you're looking for.
Distribute.
Combine like terms on the left side.
Subtract from both sides.
Subtract from both sides.
Combine like terms on the left side.
Combine like terms on the right side.
Divide both sides by to isolate .
Reduce.
So this means that Tom is 5 yrs old.
Now plug this value into to get . So 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
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