Fred and Selma's age problem

Fred is 4 times as old as his niece, Selma. Ten years from now, he will be twice as old as she will be. How old is each now? 

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x = Selma's age now
4x = Fred's age now   {Fred is 4 times as old as Selma} 

x + 10 = Selma's age in 10 years   {added 10 onto Selma’s current age above}
4x + 10 = Fred's age in 10 years   {added 10 onto Fred’s current age above}

4x + 10 = 2(x + 10)   {his age in 10 yrs is twice her age in 10 years}
4x + 10 = 2x + 20   {used distributive property}
2x + 10 = 20   {subtracted 2x from both sides}
2x = 10   {subtracted 10 from both sides}
x = 5   {divided both sides by 2}
4x = 20   {substituted 5, in for x, into 4x} 

Selma is 5 now
Fred is 20 now 

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