Question

george is 2 years older than sam and sam is 3 years older than alex. the total of their ages is 35. write and solve the equation to find the ages of george, sam, and alex

Answer 1

This breaks down into a system of equations. George will equal G, Sam will equal S and Alex will equal A.      G=S+2     S=A+3      G+S+A=35      since S=A+3, we can substitute S for (A+3). If we plug that into the G=S+2, we get G=(A+3)+2. This simplifies to G=A+5. 

our ultimate goal is to be able to substitute for two of their ages so we can solve the last equation for one age or variable. It would be easiest to solve for A. 

so far we can substitute for two variables, S=A+3.  and G=A+5

Next, we can plug this into the last equation and get 35=(A+3)+(A+5)+A
if we add like terms we get 35=3A+8. Next, we solve the equation by first subtracting 8 from each side. we then get 27=3A, then we divide each side by 3 to solve for A and get A=9.

Now we have one age, we need to find the other two. We can solve this by plugging A to the other two equations. if we do that we get S=(9)+3, or S=12. If we do it to the other equation we get G=(9)+5, or G=14 

So your final answer would be George is 14, Sam is 12, and Alex is 9.