SOLUTION: Steve is six years older than Sarah is now. In ten years he will be twice her age. Find their ages.

Question 493747: Steve is six years older than Sarah is now. In ten years he will be twice her age. Find their ages.
Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
One piece of information would have made this problem a little clearer. We read about Steve (St) and Sarah (Sa) and their current ages, and Steve's future age. Are we concerned with Sarah's future age or current age in the 2nd part of the problem? Not knowing for sure what the person posting the problem wants, we'll presume the question refers to twice Sarah's current age.
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Basic method of two equations with two variables: set one of the variables in one of the equations in terms of the other variable, including all constants and other terms, then plug that term back into the other equation so that we are solving one equation with only one variable. Once we solve for the answer to that variable, we can plug that value into both equations to determine the value for the other variable and check our work. Clear right? (Clear as mud? 8-)
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St = Sa + 6 (Steve is 6 years older than Sarah)
St + 10 = 2 * Sa (Steve in 10 years will be twice Sarah's age (today? or then?))
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first equation, recast as Sa = (St - 6)
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Take the (St - 6) term and plug into the 2nd equation:
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St + 10 = 2 * (St - 6), or
St + 10 = 2 * St - 12
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Put all the St terms one side and all the numerical terms on the other by subtracting St from both sides and adding 12 to both sides:
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10 + 12 = St
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Steve is 22 years old now and will be 32 years old in 10 years
Sarah is 16 years old now and this age (now) will be 1/2 Steve's age in 10 years
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This is a very useful method for solving all kinds of problems with two equations and two variables.
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