Find their present ages

Kristine is 4 years younger than Mario. Three years from now she will be two-thirds as old as Mario. Find their present ages.

x = Mario's age now
x - 4 = Kristine's age now 

x + 3 = Mario's age in 3 years   {added 3 on to present age}
x - 1 = Kristine's age in 3 years   {added 3 on to present age} 

x - 1 = (2/3)(x + 3)   {three years from now, she will be 2/3 his age}
3(x - 1) = 2(x + 3)   {multiplied entire equation by LCD, 3, to eliminate fraction}
3x - 3 = 2x + 6   {used distributive property}
x - 3 = 6   {subtracted 2x from each side}
x = 9   {added 3 to each side}
x - 4 = 5   {substituted 9, in for x, into x - 4} 

Mario is 9
Kristine is 5

- Algebra House