Age Problem

A man is 4-times as old as her daughter.  After 16-years, he will be twice as old as his daughter.  Find the daughter’s age.

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x = daughter's age now
4x = man's age now   {man is 4 times as old as daughter}  

x + 16 = daughter in 16 years   {added 16 onto daughter’s current age, above}
4x + 16 = man in 16 years   {added 16 onto man’s current age, above}

4x + 16 = 2(x + 16)  {after 16 years, he will be twice as old as her}
4x + 16 = 2x + 32  {used distributive property}
4x = 2x + 16  {subtracted 16 from both sides}
2x = 16  {subtracted 2x from both sides}
x = 8  {divided both sides by 2}
4x = 32  {substituted 8, in for x, into 4x}  
x = 8  {divided both sides by 4}

daughter is 8 

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