Tom and his age problem

Tom is 6 times as old as Todd. In 5 years Tom's age will be 31 years more than 2 times as old as Todd. How old is Tom?

x = Todd's age now
6x = Tom's age now   {Tom is 6 times as old as Todd}

x + 5 = Todd's age in 5 years   {added 5 onto current age}
6x + 5 = Tom's age in 5 years   {added 5 onto current age} 

6x + 5 = 2(x + 5) + 31   {in 5 years, Tom will be 31 more than 2 times Todd}
6x + 5 = 2x + 10 + 31   {used distributive property}
4x + 5 = 2x + 41   {combined like terms}
4x = 36   {subtracted 2x and 5 from each side}
x = 9   {divided each side by 2}
6x = 54   {substituted 13, in for x, into 6x} 

Tom is 54 


- Algebra House