Question 62307
Start by writing an equation for each statement, simplify each equation as much as you can:   Let the ages of the 3 cars now be: T, F, B
:
"The average age of the Johnsons' cars is 8 years."
(T + F + B)/3 = 8
Get rid of the denominator, mult eq by 3
T + F + B = 24
:
"Three years ago the Toyota was twice as old as the Ford."
T - 3 = 2(F-3)
T - 3 - 2F - 6
T = 2F - 6 + 3
T = 2F - 3
:
"Two years ago the sum of the Buick's and the Ford's ages was equal to the age of the Toyota."
(B-2) + (F-2) = (T-2)
B + F - 4 = T - 2 + 4
B + F = T+2
:
Look at the first equation: T + (F + B) = 24
We just learned that F+B = T+2
: 
Replace (F+B) with (T+2) in the 1st equation and we have:
T + (T+2) = 24
2T = 24- 2
2T = 22
T = ll yrs old is the Toyota now
:
Use the equation T = 2F - 3, to find F:
2F - 3 = 11
2F = 11 + 3
F = 14/2
F = 7 yrs old is the Ford

An easy task to find the age of the Buick:
T + F + B = 24
11 + 7 + B = 24
B = 24-18
B = 6 yrs old is the Buick
:
Check our solutions in (B-2) + (F-2) = (T-2)
4 + 5 = 9
:
:
It is often daunting to look at the big picture in these problems. Usually each statememt can be translated to a simple equation. After you have done this a logical method of substitution will emerge.